Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
564 conjugacy classes of subgroups; only the 92 normal subgroups are shown.
This group has 564 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 |
|---|---|---|
| 1. #22626584 | C2 | semidirect |
| 2. #22626240 | C2 | semidirect |
| 3. #22626165 | C2 | semidirect |
| 4. #22625004 | C2 | semidirect |
| 17. #17988841 | C4 | semidirect |
| 18. #17988840 | C4 | semidirect |
| 21. #17988837 | C4 | semidirect |
| 24. #469×C73 | C4 | semidirect |
| 36. #14556660 | D4 | semidirect |
| 42. C2×D584 | C2×C4 | semidirect |
| 60. #14556523 | C2×C4 | semidirect |
| 65. C2×D8×C73 | C2×C4 | semidirect |
| 68. #106×C73 | C2×C4 | semidirect |
| 215. C73 | #12999 | semidirect |
| 226. #469 | #64408 | semidirect |
| 242. C2×D8 | C2×#64408 | semidirect |
| 275. #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 |
| #22626240 | 2 |
| #22626165 | 2 |
| #22625004 | 2 |
| #469×D73 | 2 |
| #12999 | 73 |