Finite Group DatabasebetaFinite Group DatabasebetaOrder 30848.
210 conjugacy classes of subgroups; only the 47 normal subgroups are shown.
This group has 210 conjugacy classes of subgroups — too many to draw. Only its 47 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. #29508531 | C2 | semidirect |
| 2. #29508152 | C2 | semidirect |
| 3. C2×#21440587 | C2 | semidirect |
| 4. #29507988 | C2 | semidirect |
| 5. #29507532 | C2 | semidirect |
| 6. #29507500 | C2 | semidirect |
| 7. #359×C241 | C2 | semidirect |
| 90. C241 | #2193 | semidirect |
| 97. #359 | D241 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #29508531 | 2 |
| #29508152 | 2 |
| C2×#21440587 | 2 |
| #29507988 | 2 |
| #29507532 | 2 |
| #29507500 | 2 |
| #359×C241 | 2 |
| #2193 | 241 |