Finite Group DatabasebetaFinite Group DatabasebetaOrder 17792.
380 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 380 conjugacy classes of subgroups — too many to draw. Only its 145 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. #22581361 | C2 | semidirect |
| 4. #22581356 | C2 | semidirect |
| 5. #22581351 | C2 | semidirect |
| 6. #22581349 | C2 | semidirect |
| 9. #500×C139 | C2 | semidirect |
| 43. #14555768 | Q8 | semidirect |
| 79. C139⋊C8 | C2×Q8 | semidirect |
| 87. C8×C139 | C2×Q8 | semidirect |
| 106. C139 | #3165 | semidirect |
| 112. #500 | D139 | semidirect |
| 194. C8 | Q8×D139 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22581508 | 2 |
| C4⋊Q8×D139 | 2 |
| #22581361 | 2 |
| #22581356 | 2 |
| #22581351 | 2 |
| #22581349 | 2 |
| #22580994 | 2 |
| C4×#14555768 | 2 |
| #500×C139 | 2 |
| #3165 | 139 |