Finite Group DatabasebetaFinite Group DatabasebetaOrder 17792.
382 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 382 conjugacy classes of subgroups — too many to draw. Only its 75 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. C2×#17984867 | C2 | semidirect |
| 2. C22×#14555770 | C2 | semidirect |
| 3. C2×#17984759 | C2 | semidirect |
| 4. C2×#17984758 | C2 | semidirect |
| 5. #22580920 | C2 | semidirect |
| 6. #22580717 | C2 | semidirect |
| 7. C2×AGL(1,ℤ/8)×C139 | C2 | semidirect |
| 132. C139 | #2018 | semidirect |
| 135. C2×AGL(1,ℤ/8) | D139 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17984867 | 2 |
| C22×#14555770 | 2 |
| C2×#17984759 | 2 |
| C2×#17984758 | 2 |
| #22580920 | 2 |
| #22580717 | 2 |
| C2×AGL(1,ℤ/8)×C139 | 2 |
| #2018 | 139 |