Finite Group DatabasebetaFinite Group DatabasebetaOrder 17792.
214 conjugacy classes of subgroups; only the 61 normal subgroups are shown.
This group has 214 conjugacy classes of subgroups — too many to draw. Only its 61 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. #22581332 | C2 | semidirect |
| 2. #22581248 | C2 | semidirect |
| 4. #22580702 | C2 | semidirect |
| 5. Q8⋊(C139⋊C8) | C2 | semidirect |
| 58. D4×C139 | Q16 | semidirect |
| 87. C139 | #1632 | semidirect |
| 142. D4 | #14555775 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22581332 | 2 |
| #22581248 | 2 |
| #22581243 | 2 |
| #22580702 | 2 |
| Q8⋊(C139⋊C8) | 2 |
| D4⋊(C139⋊C8) | 2 |
| #554×C139 | 2 |
| #1632 | 139 |