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. #29508515 | C2 | semidirect |
| 2. C2×#21440667 | C2 | semidirect |
| 3. #29508286 | C2 | semidirect |
| 4. #29507735 | C2 | semidirect |
| 5. #29507721 | C2 | semidirect |
| 6. #29507487 | C2 | semidirect |
| 7. #410×C241 | C2 | semidirect |
| 56. #16838754 | D4 | semidirect |
| 58. C2×#14515349 | D4 | semidirect |
| 64. C2×Q8×C241 | D4 | semidirect |
| 66. C2×D4×C241 | D4 | semidirect |
| 142. C241 | #2008 | semidirect |
| 149. #410 | D241 | semidirect |
| 184. C2×Q8 | D964 | semidirect |
| 195. C2×D4 | D964 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #29508515 | 2 |
| C2×#21440667 | 2 |
| #29508286 | 2 |
| #29507735 | 2 |
| #29507721 | 2 |
| #29507487 | 2 |
| #410×C241 | 2 |
| #2008 | 241 |