Finite Group DatabasebetaFinite Group DatabasebetaOrder 30848.
230 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 230 conjugacy classes of subgroups — too many to draw. Only its 57 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×#21440585 | C2 | semidirect |
| 2. C2×#21440583 | C2 | semidirect |
| 3. #29507953 | C2 | semidirect |
| 4. #29507521 | C2 | semidirect |
| 5. #29507518 | C2 | semidirect |
| 6. C22⋊#16838745 | C2 | semidirect |
| 7. C2×#135×C241 | C2 | semidirect |
| 39. Q16×C241 | D4 | semidirect |
| 42. D8×C241 | D4 | semidirect |
| 89. C241 | #2186 | semidirect |
| 91. C2×#135 | D241 | semidirect |
| 123. Q16 | C22⋊D241 | semidirect |
| 128. D8 | C22⋊D241 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#21440585 | 2 |
| C2×#21440583 | 2 |
| #29507953 | 2 |
| #29507521 | 2 |
| #29507518 | 2 |
| C22⋊#16838745 | 2 |
| C2×#135×C241 | 2 |
| #2186 | 241 |