Finite Group DatabasebetaFinite Group DatabasebetaOrder 30848.
346 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 346 conjugacy classes of subgroups — too many to draw. Only its 79 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 |
|---|---|---|
| 2. #29508191 | C2 | semidirect |
| 3. #29507723 | C2 | semidirect |
| 4. #29507691 | C2 | semidirect |
| 5. #29507489 | C2 | semidirect |
| 6. #29507473 | C2 | semidirect |
| 7. #421×C241 | C2 | semidirect |
| 11. C2×#16838757 | C4 | semidirect |
| 12. C2×#16838755 | C4 | semidirect |
| 37. C2×#14515349 | C2×C4 | semidirect |
| 49. C2×Q8×C241 | C2×C4 | semidirect |
| 51. C2×D4×C241 | C2×C4 | semidirect |
| 115. C241 | #1904 | semidirect |
| 119. #421 | D241 | semidirect |
| 146. C2×Q8 | C4×D241 | semidirect |
| 154. C2×D4 | C4×D241 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#21440667 | 2 |
| #29508191 | 2 |
| #29507723 | 2 |
| #29507691 | 2 |
| #29507489 | 2 |
| #29507473 | 2 |
| #421×C241 | 2 |
| #1904 | 241 |