Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
472 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 472 conjugacy classes of subgroups — too many to draw. Only its 133 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. C2×#19153845 | C2 | semidirect |
| 2. Q8×D724 | C2 | semidirect |
| 4. #26041659 | C2 | semidirect |
| 5. #26041538 | C2 | semidirect |
| 6. #26041489 | C2 | semidirect |
| 7. #26041484 | C2 | semidirect |
| 8. #26041442 | C2 | semidirect |
| 9. #26041436 | C2 | semidirect |
| 10. #26041358 | C2 | semidirect |
| 11. C4×SD16×C181 | C2 | semidirect |
| 73. SD16×C181 | D4 | semidirect |
| 123. C4×C181 | #137 | semidirect |
| 134. C181 | #3276 | semidirect |
| 145. C4×SD16 | D181 | semidirect |
| 196. SD16 | D724 | semidirect |
| 261. C4 | #19153845 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19153845 | 2 |
| Q8×D724 | 2 |
| #26041933 | 2 |
| #26041659 | 2 |
| #26041538 | 2 |
| #26041489 | 2 |
| #26041484 | 2 |
| #26041442 | 2 |
| #26041436 | 2 |
| #26041358 | 2 |
| C4×SD16×C181 | 2 |
| #3276 | 181 |