Finite Group DatabasebetaFinite Group DatabasebetaOrder 30848.
170 conjugacy classes of subgroups; only the 47 normal subgroups are shown.
This group has 170 conjugacy classes of subgroups — too many to draw. Only its 47 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. C2×#21440583 | C2 | semidirect |
| 2. C2×#21440581 | C2 | semidirect |
| 3. #29507954 | C2 | semidirect |
| 4. #29507950 | C2 | semidirect |
| 5. #29507544 | C2 | semidirect |
| 6. #29507519 | C2 | semidirect |
| 7. #357×C241 | C2 | semidirect |
| 33. #16838745 | D4 | semidirect |
| 79. C241 | #2218 | semidirect |
| 87. #357 | D241 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#21440583 | 2 |
| C2×#21440581 | 2 |
| #29507954 | 2 |
| #29507950 | 2 |
| #29507544 | 2 |
| #29507519 | 2 |
| #357×C241 | 2 |
| #2218 | 241 |