Finite Group DatabasebetaFinite Group DatabasebetaOrder 17792.
376 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 376 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. #22581584 | C2 | semidirect |
| 3. #22581262 | C2 | semidirect |
| 4. #22581251 | C2 | semidirect |
| 5. #22581241 | C2 | semidirect |
| 6. #22581236 | C2 | semidirect |
| 7. #22580995 | C2 | semidirect |
| 8. C2×#17984773 | C2 | semidirect |
| 9. #22580981 | C2 | semidirect |
| 64. #41×C139 | Q8 | semidirect |
| 123. C139 | #3084 | semidirect |
| 166. #41 | Dic278 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22581584 | 2 |
| #22581436 | 2 |
| #22581262 | 2 |
| #22581251 | 2 |
| #22581241 | 2 |
| #22581236 | 2 |
| #22580995 | 2 |
| C2×#17984773 | 2 |
| #22580981 | 2 |
| #22580949 | 2 |
| #417×C139 | 2 |
| #3084 | 139 |