Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
354 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 354 conjugacy classes of subgroups — too many to draw. Only its 125 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. #26041986 | C2 | semidirect |
| 3. #26041684 | C2 | semidirect |
| 4. #26041621 | C2 | semidirect |
| 5. #26041593 | C2 | semidirect |
| 6. #26041575 | C2 | semidirect |
| 7. #26041570 | C2 | semidirect |
| 8. #26041525 | C2 | semidirect |
| 9. C4×#15668438 | C2 | semidirect |
| 10. #26041321 | C2 | semidirect |
| 11. #436×C181 | C2 | semidirect |
| 121. C181 | #3357 | semidirect |
| 132. #436 | D181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26041994 | 2 |
| #26041986 | 2 |
| #26041684 | 2 |
| #26041621 | 2 |
| #26041593 | 2 |
| #26041575 | 2 |
| #26041570 | 2 |
| #26041525 | 2 |
| C4×#15668438 | 2 |
| #26041321 | 2 |
| #436×C181 | 2 |
| #3357 | 181 |