Finite Group DatabasebetaFinite Group DatabasebetaOrder 30848.
442 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 442 conjugacy classes of subgroups — too many to draw. Only its 87 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×C42×D241 | C2 | semidirect |
| 3. C2×#21440570 | C2 | semidirect |
| 4. C2×#21440568 | C2 | semidirect |
| 5. #29507680 | C2 | semidirect |
| 6. #29507476 | C2 | semidirect |
| 7. #339×C241 | C2 | semidirect |
| 13. #21440622 | C4 | semidirect |
| 14. #21440617 | C4 | semidirect |
| 32. C2×Dic482 | C2×C4 | semidirect |
| 34. C2×D964 | C2×C4 | semidirect |
| 55. C4×Dic241 | D4 | semidirect |
| 61. C4⋊C4×C241 | C2×C4 | semidirect |
| 65. C42×C241 | D4 | semidirect |
| 113. C2×D241 | #104 | semidirect |
| 129. C241 | #1896 | semidirect |
| 137. #339 | D241 | semidirect |
| 186. C4⋊C4 | C4×D241 | semidirect |
| 195. C42 | D964 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #29508229 | 2 |
| C2×C42×D241 | 2 |
| C2×#21440570 | 2 |
| C2×#21440568 | 2 |
| #29507680 | 2 |
| #29507476 | 2 |
| #339×C241 | 2 |
| #1896 | 241 |