Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
374 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 374 conjugacy classes of subgroups — too many to draw. Only its 133 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. #26041989 | C2 | semidirect |
| 2. #26041685 | C2 | semidirect |
| 3. #26041675 | C2 | semidirect |
| 4. #26041579 | C2 | semidirect |
| 5. #26041569 | C2 | semidirect |
| 6. #26041566 | C2 | semidirect |
| 7. #26041556 | C2 | semidirect |
| 8. #26041410 | C2 | semidirect |
| 11. D4×Q8×C181 | C2 | semidirect |
| 45. #15668434 | Q8 | semidirect |
| 76. D724 | C2×Q8 | semidirect |
| 83. #13089678 | C2×Q8 | semidirect |
| 121. C181 | #3384 | semidirect |
| 124. D4×Q8 | D181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26041989 | 2 |
| #26041685 | 2 |
| #26041675 | 2 |
| #26041579 | 2 |
| #26041569 | 2 |
| #26041566 | 2 |
| #26041556 | 2 |
| #26041410 | 2 |
| #26041389 | 2 |
| C4×#15668434 | 2 |
| D4×Q8×C181 | 2 |
| #3384 | 181 |