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. #26041944 | C2 | semidirect |
| 3. #26041608 | C2 | semidirect |
| 4. #26041561 | C2 | semidirect |
| 5. #26041511 | C2 | semidirect |
| 6. #26041481 | C2 | semidirect |
| 7. #26041419 | C2 | semidirect |
| 8. C4×#15668438 | C2 | semidirect |
| 9. C8×D724 | C2 | semidirect |
| 10. #103×D181 | C2 | semidirect |
| 11. #487×C181 | C2 | semidirect |
| 81. Dic362 | #41 | semidirect |
| 85. D724 | SD16 | semidirect |
| 128. C181 | #3298 | semidirect |
| 132. #487 | D181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26041944 | 2 |
| #26041932 | 2 |
| #26041608 | 2 |
| #26041561 | 2 |
| #26041511 | 2 |
| #26041481 | 2 |
| #26041419 | 2 |
| C4×#15668438 | 2 |
| C8×D724 | 2 |
| #103×D181 | 2 |
| #487×C181 | 2 |
| #3298 | 181 |