Finite Group DatabasebetaFinite Group DatabasebetaOrder 17792.
552 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 552 conjugacy classes of subgroups — too many to draw. Only its 141 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×#17984874 | C2 | semidirect |
| 2. C2×#17984871 | C2 | semidirect |
| 4. C4⋊Q8×D139 | C2 | semidirect |
| 5. #22581348 | C2 | semidirect |
| 6. #22581347 | C2 | semidirect |
| 7. #22581345 | C2 | semidirect |
| 8. #22581331 | C2 | semidirect |
| 9. #22581324 | C2 | semidirect |
| 10. #22580905 | C2 | semidirect |
| 11. #497×C139 | C2 | semidirect |
| 63. #14555768 | D4 | semidirect |
| 124. Dic139 | #137 | semidirect |
| 130. C139 | #3152 | semidirect |
| 139. #497 | D139 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17984874 | 2 |
| C2×#17984871 | 2 |
| #22581502 | 2 |
| C4⋊Q8×D139 | 2 |
| #22581348 | 2 |
| #22581347 | 2 |
| #22581345 | 2 |
| #22581331 | 2 |
| #22581324 | 2 |
| #22580905 | 2 |
| #497×C139 | 2 |
| #3152 | 139 |