Finite Group DatabasebetaFinite Group DatabasebetaOrder 30848.
264 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 264 conjugacy classes of subgroups — too many to draw. Only its 81 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. #29507774 | C2 | semidirect |
| 2. C4×#16838754 | C2 | semidirect |
| 3. #29507457 | C2 | semidirect |
| 8. #21440553 | C22 | semidirect |
| 9. #21440553 | C22 | semidirect |
| 84. C241 | #1527 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #29507774 | 2 |
| C4×#16838754 | 2 |
| #29507457 | 2 |
| C2×#124×C241 | 2 |
| #1527 | 241 |