Finite Group DatabasebetaFinite Group DatabasebetaOrder 30848.
226 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 226 conjugacy classes of subgroups — too many to draw. Only its 53 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. C2×Q16×D241 | C2 | semidirect |
| 2. C2×#21440587 | C2 | semidirect |
| 3. C2×#21440585 | C2 | semidirect |
| 5. #29507520 | C2 | semidirect |
| 6. #29507496 | C2 | semidirect |
| 7. #358×C241 | C2 | semidirect |
| 32. Dic964 | D4 | semidirect |
| 43. Q16×C241 | D4 | semidirect |
| 74. C2×D241 | SD32 | semidirect |
| 86. C241 | #2185 | semidirect |
| 93. #358 | D241 | semidirect |
| 123. Q16 | D964 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×Q16×D241 | 2 |
| C2×#21440587 | 2 |
| C2×#21440585 | 2 |
| #29507954 | 2 |
| #29507520 | 2 |
| #29507496 | 2 |
| #358×C241 | 2 |
| #2185 | 241 |