Finite Group DatabasebetaFinite Group DatabasebetaOrder 17792.
380 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 380 conjugacy classes of subgroups — too many to draw. Only its 141 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 |
|---|---|---|
| 3. #22581363 | C2 | semidirect |
| 4. #22581362 | C2 | semidirect |
| 5. #22581359 | C2 | semidirect |
| 6. #22581357 | C2 | semidirect |
| 7. #22581350 | C2 | semidirect |
| 11. #501×C139 | C2 | semidirect |
| 52. #14555768 | Q8 | semidirect |
| 95. C139⋊C8 | C2×Q8 | semidirect |
| 103. C8×C139 | C2×Q8 | semidirect |
| 124. C139 | #3165 | semidirect |
| 131. #501 | D139 | semidirect |
| 228. C8 | Q8×D139 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22581509 | 2 |
| C4⋊Q8×D139 | 2 |
| #22581363 | 2 |
| #22581362 | 2 |
| #22581359 | 2 |
| #22581357 | 2 |
| #22581350 | 2 |
| #22580994 | 2 |
| #22580992 | 2 |
| #22580905 | 2 |
| #501×C139 | 2 |
| #3165 | 139 |