Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
776 conjugacy classes of subgroups; only the 104 normal subgroups are shown.
This group has 776 conjugacy classes of subgroups — too many to draw. Only its 104 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. #22624926 | C2 | direct (N × H) |
| 15. #17988498 | C4 | semidirect |
| 18. C2×#14556498 | C4 | semidirect |
| 19. C23×Q8×C73 | C4 | semidirect |
| 43. #14556498 | C2×C4 | semidirect |
| 48. C22×Q8×C73 | C2×C4 | semidirect |
| 200. C2×C73 | #1351 | semidirect |
| 211. C73 | C2×#1351 | semidirect |
| 212. C23×Q8 | #64408 | semidirect |
| 232. C22×Q8 | C2×#64408 | semidirect |
| 409. C2 | #22624926 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17989465 | 2 |
| C2×#17989431 | 2 |
| #22624926 | 2 |
| C2×#17988498 | 2 |
| C2×#1351 | 73 |