Finite Group DatabasebetaFinite Group DatabasebetaOrder 17792.
482 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 482 conjugacy classes of subgroups — too many to draw. Only its 131 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. C2×#17984865 | C2 | semidirect |
| 2. C2×Q16×D139 | C2 | semidirect |
| 3. #22581615 | C2 | semidirect |
| 4. #22581337 | C2 | semidirect |
| 5. #22581195 | C2 | semidirect |
| 6. #22581190 | C2 | semidirect |
| 7. #22581175 | C2 | semidirect |
| 8. #22581118 | C2 | semidirect |
| 9. #22581093 | C2 | semidirect |
| 10. C8×D556 | C2 | semidirect |
| 11. C4×Q16×C139 | C2 | semidirect |
| 73. Q16×C139 | D4 | semidirect |
| 120. C2×D139 | #135 | semidirect |
| 136. C139 | #3285 | semidirect |
| 147. C4×Q16 | D139 | semidirect |
| 195. Q16 | D556 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17984865 | 2 |
| C2×Q16×D139 | 2 |
| #22581615 | 2 |
| #22581337 | 2 |
| #22581195 | 2 |
| #22581190 | 2 |
| #22581175 | 2 |
| #22581118 | 2 |
| #22581093 | 2 |
| C8×D556 | 2 |
| C4×Q16×C139 | 2 |
| #3285 | 139 |