Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
416 conjugacy classes of subgroups; only the 82 normal subgroups are shown.
This group has 416 conjugacy classes of subgroups — too many to draw. Only its 82 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. #22626279 | C2 | semidirect |
| 4. #22626050 | C2 | semidirect |
| 5. #22625011 | C2 | semidirect |
| 6. #22624983 | C2 | semidirect |
| 25. #17988401 | C4 | semidirect |
| 26. #17988400 | C4 | semidirect |
| 27. #17988399 | C4 | semidirect |
| 28. #361×C73 | C4 | semidirect |
| 61. #14556531 | C2×C4 | semidirect |
| 64. #14556527 | C2×C4 | semidirect |
| 67. M32×C73 | C2×C4 | semidirect |
| 68. #108×C73 | C2×C4 | semidirect |
| 178. C73 | #12953 | semidirect |
| 198. #361 | #64408 | semidirect |
| 223. M32 | C2×#64408 | semidirect |
| 232. #108 | C2×#64408 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22626690 | 2 |
| #22626279 | 2 |
| C2×#17989505 | 2 |
| #22626050 | 2 |
| #22625011 | 2 |
| #22624983 | 2 |
| #361×D73 | 2 |
| #12953 | 73 |