Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
496 conjugacy classes of subgroups; only the 135 normal subgroups are shown.
This group has 496 conjugacy classes of subgroups — too many to draw. Only its 135 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×#19153847 | C2 | semidirect |
| 2. C2×M16×D181 | C2 | semidirect |
| 4. C2×#19153792 | C2 | semidirect |
| 5. #26041536 | C2 | semidirect |
| 6. #26041528 | C2 | semidirect |
| 7. #26041519 | C2 | semidirect |
| 8. #26041511 | C2 | semidirect |
| 9. #26041322 | C2 | semidirect |
| 10. #26041281 | C2 | semidirect |
| 11. #419×C181 | C2 | semidirect |
| 15. C2×#15668439 | C22 | semidirect |
| 16. C2×#15668436 | C22 | semidirect |
| 36. #19153749 | C22 | semidirect |
| 37. #19153747 | C22 | semidirect |
| 38. #19153741 | C22 | semidirect |
| 39. #19153738 | C22 | semidirect |
| 43. #103×C181 | C22 | semidirect |
| 44. #103×C181 | C22 | semidirect |
| 64. #15668433 | D4 | semidirect |
| 145. C2×D181 | #137 | semidirect |
| 163. C181 | #3056 | semidirect |
| 174. #419 | D181 | semidirect |
| 206. #103 | C2×D181 | semidirect |
| 207. #103 | C2×D181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19153847 | 2 |
| C2×M16×D181 | 2 |
| #26041791 | 2 |
| C2×#19153792 | 2 |
| #26041536 | 2 |
| #26041528 | 2 |
| #26041519 | 2 |
| #26041511 | 2 |
| #26041322 | 2 |
| #26041281 | 2 |
| #419×C181 | 2 |
| #3056 | 181 |