Finite Group DatabasebetaFinite Group DatabasebetaOrder 30848.
222 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 222 conjugacy classes of subgroups — too many to draw. Only its 75 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. #29507744 | C2 | semidirect |
| 5. C2×#21440553 | C2 | semidirect |
| 6. #29507481 | C2 | semidirect |
| 7. #339×C241 | C2 | semidirect |
| 14. #21440565 | C4 | semidirect |
| 15. #21440562 | C4 | semidirect |
| 90. C241 | #1938 | semidirect |
| 98. #339 | D241 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #29507744 | 2 |
| C2×#21440570 | 2 |
| #29507711 | 2 |
| #29507685 | 2 |
| C2×#21440553 | 2 |
| #29507481 | 2 |
| #339×C241 | 2 |
| #1938 | 241 |