Finite Group DatabasebetaFinite Group DatabasebetaOrder 30848.
456 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 456 conjugacy classes of subgroups — too many to draw. Only its 107 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×C4⋊C4×D241 | C2 | semidirect |
| 3. C2×#21440564 | C2 | semidirect |
| 4. C2×#21440562 | C2 | semidirect |
| 5. C2×#21440554 | C2 | semidirect |
| 6. #29507479 | C2 | semidirect |
| 7. #340×C241 | C2 | semidirect |
| 14. #21440617 | C4 | semidirect |
| 36. C2×D964 | C2×C4 | semidirect |
| 52. C4⋊Dic241 | D4 | semidirect |
| 63. C4⋊C4×C241 | C2×C4 | semidirect |
| 64. C4⋊C4×C241 | D4 | semidirect |
| 130. C2×D241 | #102 | semidirect |
| 148. C241 | #1874 | semidirect |
| 156. #340 | D241 | semidirect |
| 211. C4⋊C4 | C4×D241 | semidirect |
| 212. C4⋊C4 | D964 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#21440617 | 2 |
| C2×C4⋊C4×D241 | 2 |
| C2×#21440564 | 2 |
| C2×#21440562 | 2 |
| C2×#21440554 | 2 |
| #29507479 | 2 |
| #340×C241 | 2 |
| #1874 | 241 |