Finite Group DatabasebetaFinite Group DatabasebetaOrder 17792.
104 conjugacy classes of subgroups; only the 35 normal subgroups are shown.
This group has 104 conjugacy classes of subgroups — too many to draw. Only its 35 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. Q32×D139 | C2 | semidirect |
| 3. Dic2224 | C2 | semidirect |
| 4. #22580793 | C2 | semidirect |
| 5. #22580791 | C2 | semidirect |
| 6. #22580786 | C2 | semidirect |
| 7. SD64×C139 | C2 | semidirect |
| 51. C139 | #2264 | semidirect |
| 58. SD64 | D139 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22581382 | 2 |
| Q32×D139 | 2 |
| Dic2224 | 2 |
| #22580793 | 2 |
| #22580791 | 2 |
| #22580786 | 2 |
| SD64×C139 | 2 |
| #2264 | 139 |