Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
330 conjugacy classes of subgroups; only the 120 normal subgroups are shown.
This group has 330 conjugacy classes of subgroups — too many to draw. Only its 120 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 |
|---|---|---|
| 10. #17989512 | C4 | direct (N × H) |
| 16. #17988362 | C4 | semidirect |
| 17. #17988362 | C4 | semidirect |
| 18. C4×#11924003 | C4 | semidirect |
| 19. C4×C16×C73 | C4 | semidirect |
| 62. #11924003 | C42 | semidirect |
| 67. C16×C73 | C42 | semidirect |
| 94. C4×C73 | #365 | semidirect |
| 110. C73 | C4×#365 | semidirect |
| 122. C4×C16 | #64408 | semidirect |
| 172. C16 | C4×#64408 | semidirect |
| 202. C4 | #17989512 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17989512 | 2 |
| C4×#14556661 | 2 |
| C4×#14556659 | 2 |
| #22624996 | 2 |
| C4×#14556530 | 2 |
| C4×#365 | 73 |