Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
368 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 368 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. C2×#19153808 | C2 | semidirect |
| 3. #26041688 | C2 | semidirect |
| 4. #26041644 | C2 | semidirect |
| 5. #26041598 | C2 | semidirect |
| 6. #26041593 | C2 | semidirect |
| 7. #26041580 | C2 | semidirect |
| 8. #432×C181 | C2 | semidirect |
| 106. C181 | #3234 | semidirect |
| 115. #432 | D181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26041829 | 2 |
| C2×#19153808 | 2 |
| #26041688 | 2 |
| #26041644 | 2 |
| #26041598 | 2 |
| #26041593 | 2 |
| #26041580 | 2 |
| #432×C181 | 2 |
| #3234 | 181 |