Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
384 conjugacy classes of subgroups; only the 86 normal subgroups are shown.
This group has 384 conjugacy classes of subgroups — too many to draw. Only its 86 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 |
|---|---|---|
| 1. C4×#14556659 | C2 | semidirect |
| 2. #22625494 | C2 | semidirect |
| 4. #22624783 | C2 | semidirect |
| 15. #17988718 | C4 | semidirect |
| 16. #17988664 | C4 | semidirect |
| 19. C8×D292 | C4 | semidirect |
| 24. C8×Q8×C73 | C4 | semidirect |
| 158. C73 | #8696 | semidirect |
| 161. C8×Q8 | #64408 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#14556659 | 2 |
| #22625494 | 2 |
| #22625335 | 2 |
| #22624783 | 2 |
| #22618908 | 2 |
| #8696 | 73 |