Finite Group DatabasebetaFinite Group DatabasebetaOrder 30848.
166 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 166 conjugacy classes of subgroups — too many to draw. Only its 73 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. #29507848 | C2 | semidirect |
| 3. #29507468 | C2 | semidirect |
| 4. Q8⋊#14515349 | C2 | semidirect |
| 6. C8×#14515349 | C2 | semidirect |
| 45. #14515349 | SD16 | semidirect |
| 60. C8×C241 | M16 | semidirect |
| 77. C241 | #1590 | semidirect |
| 138. C8 | #16838754 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #29507848 | 2 |
| #29507795 | 2 |
| #29507468 | 2 |
| Q8⋊#14515349 | 2 |
| D4⋊#14515349 | 2 |
| C8×#14515349 | 2 |
| C4×SD16×C241 | 2 |
| #1590 | 241 |