Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
484 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 484 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×#19153836 | C2 | semidirect |
| 2. #26041934 | C2 | semidirect |
| 3. #26041658 | C2 | semidirect |
| 4. #26041518 | C2 | semidirect |
| 5. #26041484 | C2 | semidirect |
| 6. #26041481 | C2 | semidirect |
| 7. #26041441 | C2 | semidirect |
| 8. #26041439 | C2 | semidirect |
| 9. C4×#15668434 | C2 | semidirect |
| 10. D4×#13089678 | C2 | semidirect |
| 11. #547×C181 | C2 | semidirect |
| 53. #15668434 | D4 | semidirect |
| 127. C4×C181 | #135 | semidirect |
| 138. C181 | #3283 | semidirect |
| 142. #547 | D181 | semidirect |
| 268. C4 | #19153836 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19153836 | 2 |
| #26041934 | 2 |
| #26041658 | 2 |
| #26041518 | 2 |
| #26041484 | 2 |
| #26041481 | 2 |
| #26041441 | 2 |
| #26041439 | 2 |
| C4×#15668434 | 2 |
| D4×#13089678 | 2 |
| #547×C181 | 2 |
| #3283 | 181 |