Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
472 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 472 conjugacy classes of subgroups — too many to draw. Only its 78 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. #22626774 | C2 | semidirect |
| 2. #22625392 | C2 | semidirect |
| 3. #22625264 | C2 | semidirect |
| 4. #22625202 | C2 | semidirect |
| 5. #22624837 | C2 | semidirect |
| 6. #22624815 | C2 | semidirect |
| 215. C73 | #9350 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22626774 | 2 |
| #22625392 | 2 |
| #22625264 | 2 |
| #22625202 | 2 |
| #22624837 | 2 |
| #22624815 | 2 |
| #22619428 | 2 |
| #9350 | 73 |