Finite Group DatabasebetaFinite Group DatabasebetaOrder 17792.
350 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 350 conjugacy classes of subgroups — too many to draw. Only its 113 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 |
|---|---|---|
| 1. #22581766 | C2 | semidirect |
| 2. #22581395 | C2 | semidirect |
| 3. #22581394 | C2 | semidirect |
| 4. #22581386 | C2 | semidirect |
| 5. #22581385 | C2 | semidirect |
| 6. Q32×D139 | C2 | semidirect |
| 7. #22581369 | C2 | semidirect |
| 8. C2×Q32×C139 | C2 | semidirect |
| 81. C139 | #3417 | semidirect |
| 89. C2×Q32 | D139 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22581766 | 2 |
| #22581395 | 2 |
| #22581394 | 2 |
| #22581386 | 2 |
| #22581385 | 2 |
| Q32×D139 | 2 |
| #22581369 | 2 |
| C2×Q32×C139 | 2 |
| #3417 | 139 |