Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
372 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 372 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. #26042002 | C2 | semidirect |
| 2. #26041661 | C2 | semidirect |
| 3. #26041651 | C2 | semidirect |
| 4. #26041498 | C2 | semidirect |
| 5. #26041494 | C2 | semidirect |
| 6. #26041489 | C2 | semidirect |
| 8. Q8×#13089678 | C2 | semidirect |
| 9. C4×#15668436 | C2 | semidirect |
| 10. C4×#15668437 | C2 | semidirect |
| 11. #559×C181 | C2 | semidirect |
| 125. C181 | #3394 | semidirect |
| 127. #559 | D181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26042002 | 2 |
| #26041661 | 2 |
| #26041651 | 2 |
| #26041498 | 2 |
| #26041494 | 2 |
| #26041489 | 2 |
| #26041471 | 2 |
| Q8×#13089678 | 2 |
| C4×#15668436 | 2 |
| C4×#15668437 | 2 |
| #559×C181 | 2 |
| #3394 | 181 |