Finite Group DatabasebetaFinite Group DatabasebetaOrder 30848.
336 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 336 conjugacy classes of subgroups — too many to draw. Only its 125 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. C2×#21440575 | C2 | semidirect |
| 4. #29507479 | C2 | semidirect |
| 7. C22×#14515349 | C4 | semidirect |
| 42. #14515349 | C22⋊C4 | semidirect |
| 65. C22×C241 | #107 | semidirect |
| 83. C241 | #1808 | semidirect |
| 149. C22 | #21440575 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×#14515349 | 2 |
| C2×#21440575 | 2 |
| #29507577 | 2 |
| #29507479 | 2 |
| #380×C241 | 2 |
| #1808 | 241 |