Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
340 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 340 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 |
|---|---|---|
| 2. #26041684 | C2 | semidirect |
| 3. #26041621 | C2 | semidirect |
| 4. #26041565 | C2 | semidirect |
| 5. #26041520 | C2 | semidirect |
| 6. C4×Dic724 | C2 | semidirect |
| 7. #26041317 | C2 | semidirect |
| 82. C181 | #3342 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26041999 | 2 |
| #26041684 | 2 |
| #26041621 | 2 |
| #26041565 | 2 |
| #26041520 | 2 |
| C4×Dic724 | 2 |
| #26041317 | 2 |
| C8×D4×C181 | 2 |
| #3342 | 181 |