Finite Group DatabasebetaFinite Group DatabasebetaOrder 30848.
380 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 380 conjugacy classes of subgroups — too many to draw. Only its 107 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 |
|---|---|---|
| 3. C2×#21440567 | C2 | semidirect |
| 4. C2×#21440565 | C2 | semidirect |
| 6. #29507479 | C2 | semidirect |
| 7. #340×C241 | C2 | semidirect |
| 15. #21440622 | C4 | semidirect |
| 113. C2×D241 | #103 | semidirect |
| 131. C241 | #1892 | semidirect |
| 139. #340 | D241 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C8×D241 | 2 |
| C2×#21440622 | 2 |
| C2×#21440567 | 2 |
| C2×#21440565 | 2 |
| #29507574 | 2 |
| #29507479 | 2 |
| #340×C241 | 2 |
| #1892 | 241 |