Finite Group DatabasebetaFinite Group DatabasebetaOrder 17792.
368 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 368 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 |
|---|---|---|
| 2. #22581356 | C2 | semidirect |
| 3. #22581332 | C2 | semidirect |
| 4. #22581305 | C2 | semidirect |
| 5. #22581303 | C2 | semidirect |
| 7. C4×#14555775 | C2 | semidirect |
| 79. C2×C4×C139 | Q16 | semidirect |
| 104. C139 | #3170 | semidirect |
| 182. C2×C4 | #14555775 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22581510 | 2 |
| #22581356 | 2 |
| #22581332 | 2 |
| #22581305 | 2 |
| #22581303 | 2 |
| #22581192 | 2 |
| C4×#14555775 | 2 |
| C2×C4×C139⋊C8 | 2 |
| #533×C139 | 2 |
| #3170 | 139 |