Finite Group DatabasebetaFinite Group DatabasebetaOrder 17792.
210 conjugacy classes of subgroups; only the 49 normal subgroups are shown.
This group has 210 conjugacy classes of subgroups — too many to draw. Only its 49 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. #22581770 | C2 | semidirect |
| 2. #22581389 | C2 | semidirect |
| 3. C2×#17984786 | C2 | semidirect |
| 4. #22580768 | C2 | semidirect |
| 5. #22580759 | C2 | semidirect |
| 6. #22580737 | C2 | semidirect |
| 7. #472×C139 | C2 | semidirect |
| 90. C139 | #2193 | semidirect |
| 95. #472 | D139 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22581770 | 2 |
| #22581389 | 2 |
| C2×#17984786 | 2 |
| #22580768 | 2 |
| #22580759 | 2 |
| #22580737 | 2 |
| #472×C139 | 2 |
| #2193 | 139 |