Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
354 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 354 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. #26041836 | C2 | semidirect |
| 3. #26041587 | C2 | semidirect |
| 4. #26041565 | C2 | semidirect |
| 5. #26041560 | C2 | semidirect |
| 6. #26041520 | C2 | semidirect |
| 8. #26041502 | C2 | semidirect |
| 9. #26041490 | C2 | semidirect |
| 10. #26041485 | C2 | semidirect |
| 11. C2×C4⋊C8×C181 | C2 | semidirect |
| 133. C181 | #3248 | semidirect |
| 145. C2×C4⋊C8 | D181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26041836 | 2 |
| #26041813 | 2 |
| #26041587 | 2 |
| #26041565 | 2 |
| #26041560 | 2 |
| #26041520 | 2 |
| #26041508 | 2 |
| #26041502 | 2 |
| #26041490 | 2 |
| #26041485 | 2 |
| C2×C4⋊C8×C181 | 2 |
| #3248 | 181 |