Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
342 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 342 conjugacy classes of subgroups — too many to draw. Only its 113 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 |
|---|---|---|
| 2. #26041563 | C2 | semidirect |
| 3. #26041562 | C2 | semidirect |
| 6. #26041488 | C2 | semidirect |
| 7. #26041487 | C2 | semidirect |
| 99. C181 | #3255 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26041831 | 2 |
| #26041563 | 2 |
| #26041562 | 2 |
| #26041537 | 2 |
| #26041535 | 2 |
| #26041488 | 2 |
| #26041487 | 2 |
| #26041302 | 2 |
| #470×C181 | 2 |
| #3255 | 181 |