Finite Group DatabasebetaFinite Group DatabasebetaOrder 30848.
208 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 208 conjugacy classes of subgroups — too many to draw. Only its 57 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. #29508069 | C2 | semidirect |
| 3. #29507924 | C2 | semidirect |
| 4. #29507465 | C2 | semidirect |
| 5. #29507447 | C2 | semidirect |
| 61. D4×C241 | Q16 | semidirect |
| 88. C241 | #1644 | semidirect |
| 144. D4 | #16838760 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #29508424 | 2 |
| #29508069 | 2 |
| #29507924 | 2 |
| #29507465 | 2 |
| #29507447 | 2 |
| D4⋊#14515349 | 2 |
| #474×C241 | 2 |
| #1644 | 241 |