Finite Group DatabasebetaFinite Group DatabasebetaOrder 30848.
324 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 324 conjugacy classes of subgroups — too many to draw. Only its 93 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. #29508484 | C2 | semidirect |
| 2. #29507734 | C2 | semidirect |
| 3. #29507722 | C2 | semidirect |
| 4. C2×#21440559 | C2 | semidirect |
| 5. #29507488 | C2 | semidirect |
| 6. #29507475 | C2 | semidirect |
| 22. C2×SD16×C241 | C4 | semidirect |
| 23. C2×D8×C241 | C4 | semidirect |
| 112. C241 | #1903 | semidirect |
| 125. C2×SD16 | Dic241 | semidirect |
| 126. C2×D8 | Dic241 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #29508484 | 2 |
| #29507734 | 2 |
| #29507722 | 2 |
| C2×#21440559 | 2 |
| #29507488 | 2 |
| #29507475 | 2 |
| C2×AGL(1,ℤ/8)×C241 | 2 |
| #1903 | 241 |