Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
340 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 340 conjugacy classes of subgroups — too many to draw. Only its 117 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. #26041622 | C2 | semidirect |
| 3. #26041561 | C2 | semidirect |
| 4. #26041521 | C2 | semidirect |
| 5. C4×Dic724 | C2 | semidirect |
| 7. #26041316 | C2 | semidirect |
| 8. #500×C181 | C2 | semidirect |
| 82. C181 | #3342 | semidirect |
| 85. #500 | D181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26042003 | 2 |
| #26041622 | 2 |
| #26041561 | 2 |
| #26041521 | 2 |
| C4×Dic724 | 2 |
| C8×D724 | 2 |
| #26041316 | 2 |
| #500×C181 | 2 |
| #3342 | 181 |