Finite Group DatabasebetaFinite Group DatabasebetaOrder 30848.
408 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 408 conjugacy classes of subgroups — too many to draw. Only its 105 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. C22×#16838753 | C2 | semidirect |
| 3. C2×#21440554 | C2 | semidirect |
| 4. C2×#21440554 | C2 | semidirect |
| 5. C2×#21440554 | C2 | semidirect |
| 6. #29507472 | C2 | semidirect |
| 7. #336×C241 | C2 | semidirect |
| 52. C2×#14515349 | D4 | semidirect |
| 64. C2×C8×C241 | D4 | semidirect |
| 80. C22×D241 | M16 | semidirect |
| 104. C2×C4×C241 | M16 | semidirect |
| 151. C241 | #1870 | semidirect |
| 159. #336 | D241 | semidirect |
| 213. C2×C8 | D964 | semidirect |
| 254. C2×C4 | #16838753 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#16838753 | 2 |
| C2×C4×D964 | 2 |
| C2×#21440554 | 2 |
| #29507472 | 2 |
| #336×C241 | 2 |
| #1870 | 241 |