Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
324 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 324 conjugacy classes of subgroups — too many to draw. Only its 121 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. #26041685 | C2 | semidirect |
| 3. #26041647 | C2 | semidirect |
| 6. #26041586 | C2 | semidirect |
| 98. C181 | #3236 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19153808 | 2 |
| #26041685 | 2 |
| #26041647 | 2 |
| #26041612 | 2 |
| #26041607 | 2 |
| #26041586 | 2 |
| #26041336 | 2 |
| #533×C181 | 2 |
| #3236 | 181 |