Finite Group DatabasebetaFinite Group DatabasebetaOrder 30848.
234 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 234 conjugacy classes of subgroups — too many to draw. Only its 67 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. C4⋊C8×D241 | C2 | semidirect |
| 3. C4×#16838753 | C2 | semidirect |
| 4. Q8⋊#14515349 | C2 | semidirect |
| 5. #29507446 | C2 | semidirect |
| 6. #29507444 | C2 | semidirect |
| 7. Q8⋊C8×C241 | C2 | semidirect |
| 106. C241 | #1483 | semidirect |
| 112. Q8⋊C8 | D241 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #29508254 | 2 |
| C4⋊C8×D241 | 2 |
| C4×#16838753 | 2 |
| Q8⋊#14515349 | 2 |
| #29507446 | 2 |
| #29507444 | 2 |
| Q8⋊C8×C241 | 2 |
| #1483 | 241 |