Finite Group DatabasebetaFinite Group DatabasebetaOrder 17792.
234 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 234 conjugacy classes of subgroups — too many to draw. Only its 57 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 |
|---|---|---|
| 3. #22581160 | C2 | semidirect |
| 4. #22580699 | C2 | semidirect |
| 5. #22580685 | C2 | semidirect |
| 7. #500×C139 | C2 | semidirect |
| 55. D556 | Q16 | semidirect |
| 92. C139 | #1649 | semidirect |
| 95. #500 | D139 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22581618 | 2 |
| #22581230 | 2 |
| #22581160 | 2 |
| #22580699 | 2 |
| #22580685 | 2 |
| #22580682 | 2 |
| #500×C139 | 2 |
| #1649 | 139 |