Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
2062 conjugacy classes of subgroups; only the 382 normal subgroups are shown.
This group has 2062 conjugacy classes of subgroups — too many to draw. Only its 382 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C67 | #99 |
| commutator | C2×C4 | C23×C4×C67 |
| Frattini, cosocle | C2×D4 | C24×C67 |
| prime radical | C22×#127×C67 | C2 |
| LCS | G ▷ C2×C4 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C67 ◁ C24×C67 ◁ C23×D4×C67 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C22×#99×C67 | C2 | semidirect |
| 3. C2×#353×C67 | C2 | direct (N × H) |
| 5. C23×D4×C67 | C4 | semidirect |
| 8. C2×#127×C67 | C4 | semidirect |
| 11. C22×C42×C67 | C4 | semidirect |
| 13. C2×#99×C67 | C22 | semidirect |
| 14. #353×C67 | C22 | direct (N × H) |
| 26. C22×D4×C67 | C2×C4 | semidirect |
| 34. #127×C67 | C2×C4 | semidirect |
| 39. C2×C42×C67 | C2×C4 | semidirect |
| 41. #99×C67 | C23 | semidirect |
| 69. C2×D4×C67 | C22×C4 | semidirect |
| 83. C42×C67 | C22×C4 | semidirect |
| 136. C22×C67 | #353 | direct (N × H) |
| 144. C22×#353 | C67 | direct (N × H) |
| 150. C2×C67 | C2×#353 | direct (N × H) |
| 153. C22×#99 | C2×C67 | semidirect |
| 154. C2×#353 | C2×C67 | direct (N × H) |
| 155. C67 | C22×#353 | direct (N × H) |
| 157. C23×D4 | C4×C67 | semidirect |
| 160. C2×#127 | C4×C67 | semidirect |
| 163. C22×C42 | C4×C67 | semidirect |
| 165. C2×#99 | C22×C67 | semidirect |
| 166. #353 | C22×C67 | direct (N × H) |
| 178. C22×D4 | C2×C4×C67 | semidirect |
| 186. #127 | C2×C4×C67 | semidirect |
| 191. C2×C42 | C2×C4×C67 | semidirect |
| 193. #99 | C23×C67 | semidirect |
| 221. C2×D4 | C22×C4×C67 | semidirect |
| 235. C42 | C22×C4×C67 | semidirect |
| 288. C22 | #353×C67 | direct (N × H) |
| 301. C2 | C2×#353×C67 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#127×C67 | 2 |
| C22×#99×C67 | 2 |
| C2×#353×C67 | 2 |
| C22×#353 | 67 |