Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
420 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 420 conjugacy classes of subgroups — too many to draw. Only its 123 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. #26041934 | C2 | semidirect |
| 2. #26041933 | C2 | semidirect |
| 3. #26041630 | C2 | semidirect |
| 4. #26041615 | C2 | semidirect |
| 5. #26041560 | C2 | semidirect |
| 6. #26041525 | C2 | semidirect |
| 7. #26041485 | C2 | semidirect |
| 8. #26041426 | C2 | semidirect |
| 9. C4×D1448 | C2 | semidirect |
| 10. #26041281 | C2 | semidirect |
| 11. #436×C181 | C2 | semidirect |
| 85. D724 | #41 | semidirect |
| 132. C181 | #3330 | semidirect |
| 143. #436 | D181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26041934 | 2 |
| #26041933 | 2 |
| #26041630 | 2 |
| #26041615 | 2 |
| #26041560 | 2 |
| #26041525 | 2 |
| #26041485 | 2 |
| #26041426 | 2 |
| C4×D1448 | 2 |
| #26041281 | 2 |
| #436×C181 | 2 |
| #3330 | 181 |