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. #22580995 | C2 | semidirect |
| 3. #22580954 | C2 | semidirect |
| 4. C2×#17984758 | C2 | semidirect |
| 5. #22580855 | C2 | semidirect |
| 6. #22580713 | C2 | semidirect |
| 7. C2×#104×C139 | C2 | semidirect |
| 60. M16×C139 | D4 | semidirect |
| 130. C139 | #2037 | semidirect |
| 134. C2×#104 | D139 | semidirect |
| 181. M16 | C22⋊D139 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22581517 | 2 |
| #22580995 | 2 |
| #22580954 | 2 |
| C2×#17984758 | 2 |
| #22580855 | 2 |
| #22580713 | 2 |
| C2×#104×C139 | 2 |
| #2037 | 139 |