Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
496 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 496 conjugacy classes of subgroups — too many to draw. Only its 131 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. #26041830 | C2 | semidirect |
| 3. C4×#15668450 | C2 | semidirect |
| 4. #26041503 | C2 | semidirect |
| 5. #26041497 | C2 | semidirect |
| 6. #26041481 | C2 | semidirect |
| 7. #26041479 | C2 | semidirect |
| 8. #26041475 | C2 | semidirect |
| 9. C4⋊C8×D181 | C2 | semidirect |
| 10. #26041274 | C2 | semidirect |
| 11. #462×C181 | C2 | semidirect |
| 47. #15668450 | D4 | semidirect |
| 137. C4×C181 | #135 | semidirect |
| 150. C181 | #3035 | semidirect |
| 157. #462 | D181 | semidirect |
| 292. 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 |
| #26041830 | 2 |
| C4×#15668450 | 2 |
| #26041503 | 2 |
| #26041497 | 2 |
| #26041481 | 2 |
| #26041479 | 2 |
| #26041475 | 2 |
| C4⋊C8×D181 | 2 |
| #26041274 | 2 |
| #462×C181 | 2 |
| #3035 | 181 |