Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
416 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 416 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. C4⋊Q8×D181 | C2 | semidirect |
| 3. #26041573 | C2 | semidirect |
| 4. #26041567 | C2 | semidirect |
| 5. #26041565 | C2 | semidirect |
| 6. #26041561 | C2 | semidirect |
| 7. #26041559 | C2 | semidirect |
| 8. #26041320 | C2 | semidirect |
| 9. #26041301 | C2 | semidirect |
| 11. #474×C181 | C2 | semidirect |
| 44. #15668448 | Q8 | semidirect |
| 86. Dic362 | C2×Q8 | semidirect |
| 105. D4×C181 | C2×Q8 | semidirect |
| 137. C181 | #3079 | semidirect |
| 146. #474 | D181 | semidirect |
| 229. D4 | Q8×D181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4⋊Q8×D181 | 2 |
| C4×#15668448 | 2 |
| #26041573 | 2 |
| #26041567 | 2 |
| #26041565 | 2 |
| #26041561 | 2 |
| #26041559 | 2 |
| #26041320 | 2 |
| #26041301 | 2 |
| #26041277 | 2 |
| #474×C181 | 2 |
| #3079 | 181 |