Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
374 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 374 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 |
|---|---|---|
| 1. #26041999 | C2 | semidirect |
| 3. #26041684 | C2 | semidirect |
| 4. #26041615 | C2 | semidirect |
| 5. #26041604 | C2 | semidirect |
| 6. #26041565 | C2 | semidirect |
| 7. #26041560 | C2 | semidirect |
| 8. #26041525 | C2 | semidirect |
| 9. C4×#15668438 | C2 | semidirect |
| 10. #26041321 | C2 | semidirect |
| 11. #436×C181 | C2 | semidirect |
| 99. C8×C181 | #41 | semidirect |
| 122. C181 | #3353 | semidirect |
| 133. #436 | D181 | semidirect |
| 222. C8 | #15668448 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26041999 | 2 |
| #26041933 | 2 |
| #26041684 | 2 |
| #26041615 | 2 |
| #26041604 | 2 |
| #26041565 | 2 |
| #26041560 | 2 |
| #26041525 | 2 |
| C4×#15668438 | 2 |
| #26041321 | 2 |
| #436×C181 | 2 |
| #3353 | 181 |