Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
240 conjugacy classes of subgroups; only the 64 normal subgroups are shown.
This group has 240 conjugacy classes of subgroups — too many to draw. Only its 64 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. #22625563 | C2 | semidirect |
| 2. #22625512 | C2 | semidirect |
| 3. #22624965 | C2 | semidirect |
| 4. #22624886 | C2 | semidirect |
| 5. #22624886 | C2 | semidirect |
| 6. #22624845 | C2 | semidirect |
| 59. D584 | M16 | semidirect |
| 119. C73 | #12073 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22625563 | 2 |
| #22625512 | 2 |
| #22624965 | 2 |
| #22624886 | 2 |
| #22624845 | 2 |
| #22611777 | 2 |
| #12073 | 73 |