Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
372 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 372 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 |
|---|---|---|
| 1. #26042002 | C2 | semidirect |
| 2. #26041641 | C2 | semidirect |
| 3. #26041631 | C2 | semidirect |
| 4. #26041571 | C2 | semidirect |
| 5. #26041556 | C2 | semidirect |
| 7. #26041484 | C2 | semidirect |
| 8. #26041410 | C2 | semidirect |
| 9. #26041379 | C2 | semidirect |
| 11. D4×Q8×C181 | C2 | semidirect |
| 122. C181 | #3367 | semidirect |
| 125. D4×Q8 | D181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26042002 | 2 |
| #26041641 | 2 |
| #26041631 | 2 |
| #26041571 | 2 |
| #26041556 | 2 |
| #26041494 | 2 |
| #26041484 | 2 |
| #26041410 | 2 |
| #26041379 | 2 |
| C4×#15668434 | 2 |
| D4×Q8×C181 | 2 |
| #3367 | 181 |