Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
512 conjugacy classes of subgroups; only the 92 normal subgroups are shown.
This group has 512 conjugacy classes of subgroups — too many to draw. Only its 92 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 |
|---|---|---|
| 2. #22626241 | C2 | semidirect |
| 4. #22625004 | C2 | semidirect |
| 17. #17988846 | C4 | semidirect |
| 18. #17988845 | C4 | semidirect |
| 21. #17988842 | C4 | semidirect |
| 24. #470×C73 | C4 | semidirect |
| 41. C2×Dic292 | C2×C4 | semidirect |
| 60. #14556523 | C2×C4 | semidirect |
| 65. C2×Q16×C73 | C2×C4 | semidirect |
| 68. #106×C73 | C2×C4 | semidirect |
| 200. C73 | #13000 | semidirect |
| 211. #470 | #64408 | semidirect |
| 226. C2×Q16 | C2×#64408 | semidirect |
| 260. #106 | C2×#64408 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22626584 | 2 |
| #22626241 | 2 |
| #22626165 | 2 |
| #22625004 | 2 |
| #470×D73 | 2 |
| #13000 | 73 |