Finite Group DatabasebetaFinite Group DatabasebetaOrder 30848.
142 conjugacy classes of subgroups; only the 49 normal subgroups are shown.
This group has 142 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 |
|---|---|---|
| 2. #29507755 | C2 | semidirect |
| 3. #29507545 | C2 | semidirect |
| 4. #29507543 | C2 | semidirect |
| 5. #29507519 | C2 | semidirect |
| 6. #29507519 | C2 | semidirect |
| 7. C22⋊C16×C241 | C2 | semidirect |
| 69. C241 | #2234 | semidirect |
| 77. C22⋊C16 | D241 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #29507953 | 2 |
| #29507755 | 2 |
| #29507545 | 2 |
| #29507543 | 2 |
| #29507519 | 2 |
| C22⋊C16×C241 | 2 |
| #2234 | 241 |