Finite Group DatabasebetaFinite Group DatabasebetaOrder 30848.
180 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 180 conjugacy classes of subgroups — too many to draw. Only its 83 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 |
|---|---|---|
| 4. #29507469 | C2 | semidirect |
| 5. #29507468 | C2 | semidirect |
| 6. #29507467 | C2 | semidirect |
| 7. #335×C241 | C2 | semidirect |
| 27. #16838753 | C8 | semidirect |
| 53. #14515349 | C2×C8 | semidirect |
| 60. C8×C241 | C2×C8 | semidirect |
| 77. C241 | #1565 | semidirect |
| 83. #335 | D241 | semidirect |
| 138. C8 | C8×D241 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #29507769 | 2 |
| C4⋊C8×D241 | 2 |
| C4×#16838753 | 2 |
| #29507469 | 2 |
| #29507468 | 2 |
| #29507467 | 2 |
| #335×C241 | 2 |
| #1565 | 241 |