Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
360 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 121 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. #26041813 | C2 | semidirect |
| 2. #26041587 | C2 | semidirect |
| 3. #26041580 | C2 | semidirect |
| 4. #26041520 | C2 | semidirect |
| 6. #26041508 | C2 | semidirect |
| 7. #26041502 | C2 | semidirect |
| 8. #26041495 | C2 | semidirect |
| 9. C2×C4⋊C8×C181 | C2 | semidirect |
| 106. C181 | #3250 | semidirect |
| 116. C2×C4⋊C8 | D181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26041813 | 2 |
| #26041587 | 2 |
| #26041580 | 2 |
| #26041520 | 2 |
| #26041515 | 2 |
| #26041508 | 2 |
| #26041502 | 2 |
| #26041495 | 2 |
| C2×C4⋊C8×C181 | 2 |
| #3250 | 181 |