Finite Group DatabasebetaFinite Group DatabasebetaOrder 17792.
426 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 426 conjugacy classes of subgroups — too many to draw. Only its 125 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. #22581624 | C2 | semidirect |
| 2. D4×Dic278 | C2 | semidirect |
| 3. #22581300 | C2 | semidirect |
| 4. #22581298 | C2 | semidirect |
| 5. #22581233 | C2 | semidirect |
| 6. #22581232 | C2 | semidirect |
| 7. #22581148 | C2 | semidirect |
| 8. #22581146 | C2 | semidirect |
| 9. C8×Dic278 | C2 | semidirect |
| 10. #22581033 | C2 | semidirect |
| 11. C4×D8×C139 | C2 | semidirect |
| 78. Dic278 | D8 | semidirect |
| 96. D4×C139 | #41 | semidirect |
| 131. C139 | #3358 | semidirect |
| 143. C4×D8 | D139 | semidirect |
| 222. D4 | #14555785 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22581624 | 2 |
| D4×Dic278 | 2 |
| #22581300 | 2 |
| #22581298 | 2 |
| #22581233 | 2 |
| #22581232 | 2 |
| #22581148 | 2 |
| #22581146 | 2 |
| C8×Dic278 | 2 |
| #22581033 | 2 |
| C4×D8×C139 | 2 |
| #3358 | 139 |