Finite Group DatabasebetaFinite Group DatabasebetaOrder 30848.
380 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 380 conjugacy classes of subgroups — too many to draw. Only its 69 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. #29508517 | C2 | semidirect |
| 2. C2×#21440668 | C2 | semidirect |
| 3. #29508284 | C2 | semidirect |
| 4. #29507735 | C2 | semidirect |
| 5. #29507690 | C2 | semidirect |
| 6. #29507488 | C2 | semidirect |
| 7. #418×C241 | C2 | semidirect |
| 40. C2×Dic482 | D4 | semidirect |
| 42. C2×D964 | D4 | semidirect |
| 55. #16838754 | D4 | semidirect |
| 71. C2×C8×C241 | D4 | semidirect |
| 142. C241 | #2008 | semidirect |
| 148. #418 | D241 | semidirect |
| 210. C2×C8 | C22⋊D241 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #29508517 | 2 |
| C2×#21440668 | 2 |
| #29508284 | 2 |
| #29507735 | 2 |
| #29507690 | 2 |
| #29507488 | 2 |
| #418×C241 | 2 |
| #2008 | 241 |