Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
540 conjugacy classes of subgroups; only the 82 normal subgroups are shown.
This group has 540 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 |
|---|---|---|
| 1. #22626858 | C2 | semidirect |
| 2. #22626073 | C2 | semidirect |
| 3. #22625438 | C2 | semidirect |
| 4. #22625268 | C2 | semidirect |
| 5. #22624839 | C2 | semidirect |
| 6. #22624815 | C2 | semidirect |
| 184. D292 | #100 | semidirect |
| 241. C73 | #9359 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22626858 | 2 |
| #22626073 | 2 |
| #22625438 | 2 |
| #22625268 | 2 |
| #22624839 | 2 |
| #22624815 | 2 |
| #22619410 | 2 |
| #9359 | 73 |