Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
412 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 412 conjugacy classes of subgroups — too many to draw. Only its 99 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. C22×#15668432 | C2 | semidirect |
| 3. C2×#19153738 | C2 | semidirect |
| 4. C2×#19153736 | C2 | semidirect |
| 5. #26041136 | C2 | semidirect |
| 6. #26041041 | C2 | semidirect |
| 7. #340×C181 | C2 | semidirect |
| 16. #19153791 | C4 | semidirect |
| 48. C2×#13089678 | D4 | semidirect |
| 58. C2×C8×C181 | D4 | semidirect |
| 145. C181 | #1895 | semidirect |
| 153. #340 | D181 | semidirect |
| 200. C2×C8 | D724 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#15668432 | 2 |
| C2×#19153791 | 2 |
| C2×#19153738 | 2 |
| C2×#19153736 | 2 |
| #26041136 | 2 |
| #26041041 | 2 |
| #340×C181 | 2 |
| #1895 | 181 |