Finite Group DatabasebetaFinite Group DatabasebetaOrder 17792.
424 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 424 conjugacy classes of subgroups — too many to draw. Only its 133 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. #22581266 | C2 | semidirect |
| 3. #22581248 | C2 | semidirect |
| 4. #22581153 | C2 | semidirect |
| 5. #22581092 | C2 | semidirect |
| 6. #22581051 | C2 | semidirect |
| 7. #22581010 | C2 | semidirect |
| 8. C2×C4×Q8×C139 | C2 | semidirect |
| 76. Q8×C139 | #41 | semidirect |
| 111. C139 | #3112 | semidirect |
| 114. C2×C4×Q8 | D139 | semidirect |
| 181. Q8 | #14555785 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22581503 | 2 |
| #22581266 | 2 |
| #22581248 | 2 |
| #22581153 | 2 |
| #22581092 | 2 |
| #22581051 | 2 |
| #22581010 | 2 |
| C2×C4×Q8×C139 | 2 |
| #3112 | 139 |