Finite Group DatabasebetaFinite Group DatabasebetaOrder 27392.
458 conjugacy classes of subgroups; only the 90 normal subgroups are shown.
This group has 458 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 | C22×C107 | #447 |
| commutator, Frattini, cosocle | C4×C8 | C23×C107 |
| LCS | G ▷ C4×C8 ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C107 ◁ C42×C107 ◁ C8×D4×C107 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. D4×D8×C107 | C2 | semidirect |
| 2. C107×#2246 | C2 | semidirect |
| 3. C107×#2206 | C2 | semidirect |
| 4. C107×#1667 | C2 | semidirect |
| 5. C107×#1361 | C2 | semidirect |
| 6. C107×#1331 | C2 | semidirect |
| 7. C107×D4⋊C16 | C2 | semidirect |
| 13. #493×C107 | C22 | semidirect |
| 20. C4⋊C16×C107 | C22 | semidirect |
| 22. C4×C16×C107 | C22 | semidirect |
| 23. #335×C107 | C22 | semidirect |
| 82. D8×C107 | D8 | semidirect |
| 119. D4×C107 | D16 | semidirect |
| 155. #12316 | C107 | direct (N × H) |
| 163. D4×D8 | C2×C107 | semidirect |
| 164. #2246 | C2×C107 | semidirect |
| 165. #2206 | C2×C107 | semidirect |
| 166. #1667 | C2×C107 | semidirect |
| 167. #1361 | C2×C107 | semidirect |
| 168. #1331 | C2×C107 | semidirect |
| 169. D4⋊C16 | C2×C107 | semidirect |
| 170. C107 | #12316 | direct (N × H) |
| 176. #493 | C22×C107 | semidirect |
| 183. C4⋊C16 | C22×C107 | semidirect |
| 185. C4×C16 | C22×C107 | semidirect |
| 186. #335 | C22×C107 | semidirect |
| 245. D8 | D8×C107 | semidirect |
| 282. D4 | D16×C107 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D4×D8×C107 | 2 |
| C107×#2246 | 2 |
| C107×#2206 | 2 |
| C107×#1667 | 2 |
| C107×#1361 | 2 |
| C107×#1331 | 2 |
| C107×D4⋊C16 | 2 |
| #12316 | 107 |