Finite Group DatabasebetaFinite Group DatabasebetaOrder 17792.
372 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 372 conjugacy classes of subgroups — too many to draw. Only its 117 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. #22581673 | C2 | semidirect |
| 2. D4×Dic278 | C2 | semidirect |
| 3. #22581311 | C2 | semidirect |
| 4. #22581304 | C2 | semidirect |
| 5. #22581247 | C2 | semidirect |
| 6. #22581233 | C2 | semidirect |
| 8. #22581158 | C2 | semidirect |
| 9. #22581083 | C2 | semidirect |
| 10. #22581050 | C2 | semidirect |
| 122. C139 | #3367 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22581673 | 2 |
| D4×Dic278 | 2 |
| #22581311 | 2 |
| #22581304 | 2 |
| #22581247 | 2 |
| #22581233 | 2 |
| #22581166 | 2 |
| #22581158 | 2 |
| #22581083 | 2 |
| #22581050 | 2 |
| C4×D8×C139 | 2 |
| #3367 | 139 |