Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
690 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 690 conjugacy classes of subgroups — too many to draw. Only its 111 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. #22618960 | C2 | semidirect |
| 2. #22608645 | C2 | semidirect |
| 3. #22608272 | C2 | semidirect |
| 4. #22607787 | C2 | semidirect |
| 26. C4⋊#10596831 | D4 | semidirect |
| 192. C73 | #9457 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22618960 | 2 |
| #22608645 | 2 |
| #22608272 | 2 |
| #22607787 | 2 |
| C73×#2541 | 2 |
| #9457 | 73 |