Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
494 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 494 conjugacy classes of subgroups — too many to draw. Only its 125 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×#19153839 | C2 | semidirect |
| 2. #26041951 | C2 | semidirect |
| 3. #26041932 | C2 | semidirect |
| 4. #26041653 | C2 | semidirect |
| 5. #26041511 | C2 | semidirect |
| 6. #26041475 | C2 | semidirect |
| 7. #26041440 | C2 | semidirect |
| 8. #26041427 | C2 | semidirect |
| 9. C4×#15668436 | C2 | semidirect |
| 10. #26041344 | C2 | semidirect |
| 11. #462×C181 | C2 | semidirect |
| 60. #15668436 | D4 | semidirect |
| 129. C4×C181 | #135 | semidirect |
| 140. C181 | #3284 | semidirect |
| 147. #462 | D181 | semidirect |
| 272. C4 | #19153839 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19153839 | 2 |
| #26041951 | 2 |
| #26041932 | 2 |
| #26041653 | 2 |
| #26041511 | 2 |
| #26041475 | 2 |
| #26041440 | 2 |
| #26041427 | 2 |
| C4×#15668436 | 2 |
| #26041344 | 2 |
| #462×C181 | 2 |
| #3284 | 181 |