Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
494 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 494 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×#19153837 | C2 | semidirect |
| 2. #26041951 | C2 | semidirect |
| 3. #26041933 | C2 | semidirect |
| 4. #26041652 | C2 | semidirect |
| 5. #26041509 | C2 | semidirect |
| 6. #26041489 | C2 | semidirect |
| 7. #26041474 | C2 | semidirect |
| 8. #26041444 | C2 | semidirect |
| 9. #26041425 | C2 | semidirect |
| 10. C8×D724 | C2 | semidirect |
| 11. C4×SD16×C181 | C2 | semidirect |
| 73. SD16×C181 | D4 | semidirect |
| 129. C4×C181 | #135 | semidirect |
| 140. C181 | #3284 | semidirect |
| 151. C4×SD16 | D181 | semidirect |
| 204. SD16 | D724 | semidirect |
| 272. C4 | #19153837 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19153837 | 2 |
| #26041951 | 2 |
| #26041933 | 2 |
| #26041652 | 2 |
| #26041509 | 2 |
| #26041489 | 2 |
| #26041474 | 2 |
| #26041444 | 2 |
| #26041425 | 2 |
| C8×D724 | 2 |
| C4×SD16×C181 | 2 |
| #3284 | 181 |