Finite Group DatabasebetaFinite Group DatabasebetaOrder 30848.
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×#21440667 | C2 | semidirect |
| 2. C22×#16838755 | C2 | semidirect |
| 3. C2×#21440559 | C2 | semidirect |
| 4. C2×#21440558 | C2 | semidirect |
| 5. #29507684 | C2 | semidirect |
| 6. #29507481 | C2 | semidirect |
| 7. C2×AGL(1,ℤ/8)×C241 | C2 | semidirect |
| 132. C241 | #2018 | semidirect |
| 135. C2×AGL(1,ℤ/8) | D241 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#21440667 | 2 |
| C22×#16838755 | 2 |
| C2×#21440559 | 2 |
| C2×#21440558 | 2 |
| #29507684 | 2 |
| #29507481 | 2 |
| C2×AGL(1,ℤ/8)×C241 | 2 |
| #2018 | 241 |