Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
386 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 386 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. #26041574 | C2 | semidirect |
| 3. #26041556 | C2 | semidirect |
| 4. #26041527 | C2 | semidirect |
| 5. #26041481 | C2 | semidirect |
| 6. #26041479 | C2 | semidirect |
| 7. #26041303 | C2 | semidirect |
| 8. #533×C181 | C2 | semidirect |
| 112. C181 | #3254 | semidirect |
| 114. #533 | D181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26041829 | 2 |
| #26041574 | 2 |
| #26041556 | 2 |
| #26041527 | 2 |
| #26041481 | 2 |
| #26041479 | 2 |
| #26041303 | 2 |
| #533×C181 | 2 |
| #3254 | 181 |