Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
420 conjugacy classes of subgroups; only the 90 normal subgroups are shown.
This group has 420 conjugacy classes of subgroups — too many to draw. Only its 90 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C67 | C2×#353 |
| commutator | C42 | C22×C4×C67 |
| Frattini, cosocle | #124 | C23×C67 |
| prime radical | C67×#3153 | C2 |
| LCS | G ▷ C42 ▷ C2×C4 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C67 ◁ C23×C67 ◁ C22×C4×C67 ◁ C2×#124×C67 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×#355×C67 | C2 | semidirect |
| 3. C2×#354×C67 | C2 | semidirect |
| 4. C67×#1407 | C2 | semidirect |
| 5. C67×#1406 | C2 | semidirect |
| 8. #532×C67 | C4 | semidirect |
| 10. #497×C67 | C4 | semidirect |
| 12. #496×C67 | C4 | semidirect |
| 18. C4×M16×C67 | C4 | semidirect |
| 40. C4⋊Q8×C67 | C2×C4 | semidirect |
| 41. #127×C67 | C2×C4 | semidirect |
| 57. #97×C67 | C2×C4 | semidirect |
| 58. #97×C67 | C2×C4 | semidirect |
| 169. #13578 | C67 | direct (N × H) |
| 178. C2×#355 | C2×C67 | semidirect |
| 179. C2×#354 | C2×C67 | semidirect |
| 180. #1407 | C2×C67 | semidirect |
| 181. #1406 | C2×C67 | semidirect |
| 182. C67 | #13578 | direct (N × H) |
| 185. #532 | C4×C67 | semidirect |
| 187. #497 | C4×C67 | semidirect |
| 189. #496 | C4×C67 | semidirect |
| 195. C4×M16 | C4×C67 | semidirect |
| 217. C4⋊Q8 | C2×C4×C67 | semidirect |
| 218. #127 | C2×C4×C67 | semidirect |
| 234. #97 | C2×C4×C67 | semidirect |
| 235. #97 | C2×C4×C67 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C67×#3153 | 2 |
| C2×#355×C67 | 2 |
| C2×#354×C67 | 2 |
| C67×#1407 | 2 |
| C67×#1406 | 2 |
| #13578 | 67 |