Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
316 conjugacy classes of subgroups; only the 54 normal subgroups are shown.
This group has 316 conjugacy classes of subgroups — too many to draw. Only its 54 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. #22626234 | C2 | semidirect |
| 2. #22626227 | C2 | semidirect |
| 3. #22625074 | C2 | semidirect |
| 4. #22625073 | C2 | semidirect |
| 5. #22625067 | C2 | semidirect |
| 6. #22625067 | C2 | semidirect |
| 165. C73 | #13611 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22626234 | 2 |
| #22626227 | 2 |
| #22625074 | 2 |
| #22625073 | 2 |
| #22625067 | 2 |
| #22620995 | 2 |
| #13611 | 73 |