Finite Group DatabasebetaFinite Group DatabasebetaOrder 30848.
166 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 166 conjugacy classes of subgroups — too many to draw. Only its 65 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 |
|---|---|---|
| 3. #29507469 | C2 | semidirect |
| 4. Q8⋊#14515349 | C2 | semidirect |
| 6. #29507439 | C2 | semidirect |
| 7. C8×Q8×C241 | C2 | semidirect |
| 52. Q8×C241 | M16 | semidirect |
| 77. C241 | #1588 | semidirect |
| 79. C8×Q8 | D241 | semidirect |
| 121. Q8 | #16838753 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#16838757 | 2 |
| #29507796 | 2 |
| #29507469 | 2 |
| Q8⋊#14515349 | 2 |
| #29507444 | 2 |
| #29507439 | 2 |
| C8×Q8×C241 | 2 |
| #1588 | 241 |