Finite Group DatabasebetaFinite Group DatabasebetaOrder 17792.
282 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 282 conjugacy classes of subgroups — too many to draw. Only its 69 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. #22581581 | C2 | semidirect |
| 4. #22580721 | C2 | semidirect |
| 5. #22580714 | C2 | semidirect |
| 6. #22580712 | C2 | semidirect |
| 49. C2×D4×C139 | Q8 | semidirect |
| 112. C139 | #2027 | semidirect |
| 145. C2×D4 | Dic278 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22581581 | 2 |
| #22580958 | 2 |
| #22580856 | 2 |
| #22580721 | 2 |
| #22580714 | 2 |
| #22580712 | 2 |
| #418×C139 | 2 |
| #2027 | 139 |