Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
492 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 101 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. #22609923 | C2 | semidirect |
| 2. #22608701 | C2 | semidirect |
| 3. #22608599 | C2 | semidirect |
| 4. #22608599 | C2 | semidirect |
| 5. #22608322 | C2 | semidirect |
| 6. #22607828 | C2 | semidirect |
| 191. C73 | #10441 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22609923 | 2 |
| #22608701 | 2 |
| #22608599 | 2 |
| #22608322 | 2 |
| #22607828 | 2 |
| C2×#459×C73 | 2 |
| #10441 | 73 |