Finite Group DatabasebetaFinite Group DatabasebetaOrder 17792.
412 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 412 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 |
|---|---|---|
| 1. #22581510 | C2 | semidirect |
| 2. #22581349 | C2 | semidirect |
| 3. #22581325 | C2 | semidirect |
| 4. #22581305 | C2 | semidirect |
| 5. #22581299 | C2 | semidirect |
| 6. #22581180 | C2 | semidirect |
| 7. C4×#14555773 | C2 | semidirect |
| 8. C2×C4×C139⋊C8 | C2 | semidirect |
| 72. C139⋊C8 | #41 | semidirect |
| 84. C2×C4×C139 | SD16 | semidirect |
| 112. C139 | #3167 | semidirect |
| 195. C2×C4 | #14555773 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22581510 | 2 |
| #22581349 | 2 |
| #22581325 | 2 |
| #22581305 | 2 |
| #22581299 | 2 |
| #22581180 | 2 |
| C4×#14555773 | 2 |
| C2×C4×C139⋊C8 | 2 |
| #532×C139 | 2 |
| #3167 | 139 |