Finite Group DatabasebetaFinite Group DatabasebetaOrder 17792.
484 conjugacy classes of subgroups; only the 175 normal subgroups are shown.
This group has 484 conjugacy classes of subgroups — too many to draw. Only its 175 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. #22581435 | C2 | semidirect |
| 3. #22581066 | C2 | semidirect |
| 4. #22581064 | C2 | semidirect |
| 5. #22581060 | C2 | semidirect |
| 6. C4×#14555772 | C2 | semidirect |
| 7. #22581038 | C2 | semidirect |
| 8. #106×D139 | C2 | semidirect |
| 9. #22580953 | C2 | semidirect |
| 10. #22580910 | C2 | semidirect |
| 11. #441×C139 | C2 | semidirect |
| 13. #17984865 | C4 | semidirect |
| 41. #14555786 | C2×C4 | semidirect |
| 49. #14555772 | C2×C4 | semidirect |
| 50. D1112 | C2×C4 | semidirect |
| 54. C8×D139 | C2×C4 | semidirect |
| 65. Q16×C139 | C2×C4 | semidirect |
| 114. C139 | #2952 | semidirect |
| 121. #441 | D139 | semidirect |
| 165. Q16 | C4×D139 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17984865 | 2 |
| #22581435 | 2 |
| #22581066 | 2 |
| #22581064 | 2 |
| #22581060 | 2 |
| C4×#14555772 | 2 |
| #22581038 | 2 |
| #106×D139 | 2 |
| #22580953 | 2 |
| #22580910 | 2 |
| #441×C139 | 2 |
| #2952 | 139 |