Finite Group DatabasebetaFinite Group DatabasebetaOrder 17792.
272 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 272 conjugacy classes of subgroups — too many to draw. Only its 73 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. #22580799 | C2 | semidirect |
| 3. #22580688 | C2 | semidirect |
| 4. #432×C139 | C2 | semidirect |
| 6. #17984842 | C4 | semidirect |
| 7. #17984839 | C4 | semidirect |
| 12. C4×D556 | C4 | semidirect |
| 83. C139 | #1505 | semidirect |
| 86. #432 | D139 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22581503 | 2 |
| #22580799 | 2 |
| #22580688 | 2 |
| #432×C139 | 2 |
| #1505 | 139 |