Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
498 conjugacy classes of subgroups; only the 112 normal subgroups are shown.
This group has 498 conjugacy classes of subgroups — too many to draw. Only its 112 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. M32×#64408 | C2 | semidirect |
| 4. #108×#64408 | C2 | semidirect |
| 5. #22625007 | C2 | semidirect |
| 6. #22625006 | C2 | semidirect |
| 19. #17989505 | C4 | semidirect |
| 26. #17988401 | C4 | semidirect |
| 27. #17988400 | C4 | semidirect |
| 28. #17988399 | C4 | semidirect |
| 29. #361×C73 | C4 | semidirect |
| 40. #14556666 | C2×C4 | semidirect |
| 44. #14556661 | C2×C4 | semidirect |
| 64. #14556531 | C2×C4 | semidirect |
| 67. #14556527 | C2×C4 | semidirect |
| 70. M32×C73 | C2×C4 | semidirect |
| 71. #108×C73 | C2×C4 | semidirect |
| 175. #64408 | #361 | direct (N × H) |
| 195. C73 | C4×#361 | semidirect |
| 214. #361 | #64408 | direct (N × H) |
| 242. M32 | C2×#64408 | semidirect |
| 249. #108 | C2×#64408 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D8×#64408 | 2 |
| D73⋊#361 | 2 |
| M32×#64408 | 2 |
| #108×#64408 | 2 |
| #22625007 | 2 |
| #22625006 | 2 |
| #361×D73 | 2 |
| C4×#361 | 73 |