Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
372 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 372 conjugacy classes of subgroups — too many to draw. Only its 123 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. #26042014 | C2 | semidirect |
| 2. #26041661 | C2 | semidirect |
| 3. #26041653 | C2 | semidirect |
| 4. #26041501 | C2 | semidirect |
| 5. #26041491 | C2 | semidirect |
| 6. #26041486 | C2 | semidirect |
| 8. Q8×#13089678 | C2 | semidirect |
| 9. C4×#15668436 | C2 | semidirect |
| 10. C4×#15668437 | C2 | semidirect |
| 11. #556×C181 | C2 | semidirect |
| 125. C181 | #3394 | semidirect |
| 128. #556 | D181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26042014 | 2 |
| #26041661 | 2 |
| #26041653 | 2 |
| #26041501 | 2 |
| #26041491 | 2 |
| #26041486 | 2 |
| #26041474 | 2 |
| Q8×#13089678 | 2 |
| C4×#15668436 | 2 |
| C4×#15668437 | 2 |
| #556×C181 | 2 |
| #3394 | 181 |