Finite Group DatabasebetaFinite Group DatabasebetaOrder 17792.
326 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 326 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 |
|---|---|---|
| 2. C2×#17984768 | C2 | semidirect |
| 3. #22580952 | C2 | semidirect |
| 4. C2×#17984758 | C2 | semidirect |
| 5. #22580854 | C2 | semidirect |
| 6. #22580712 | C2 | semidirect |
| 7. #428×C139 | C2 | semidirect |
| 56. M16×C139 | D4 | semidirect |
| 130. C139 | #2037 | semidirect |
| 133. #428 | D139 | semidirect |
| 181. M16 | D556 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22581522 | 2 |
| C2×#17984768 | 2 |
| #22580952 | 2 |
| C2×#17984758 | 2 |
| #22580854 | 2 |
| #22580712 | 2 |
| #428×C139 | 2 |
| #2037 | 139 |