Finite Group DatabasebetaFinite Group DatabasebetaOrder 17792.
386 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 386 conjugacy classes of subgroups — too many to draw. Only its 125 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. #22581248 | C2 | semidirect |
| 3. #22581230 | C2 | semidirect |
| 4. #22581201 | C2 | semidirect |
| 5. #22581155 | C2 | semidirect |
| 6. #22581153 | C2 | semidirect |
| 7. #22580977 | C2 | semidirect |
| 8. #533×C139 | C2 | semidirect |
| 112. C139 | #3254 | semidirect |
| 114. #533 | D139 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22581503 | 2 |
| #22581248 | 2 |
| #22581230 | 2 |
| #22581201 | 2 |
| #22581155 | 2 |
| #22581153 | 2 |
| #22580977 | 2 |
| #533×C139 | 2 |
| #3254 | 139 |