Finite Group DatabasebetaFinite Group DatabasebetaOrder 30848.
198 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 198 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. #29508093 | C2 | semidirect |
| 2. #29507912 | C2 | semidirect |
| 3. #29507795 | C2 | semidirect |
| 4. #29507467 | C2 | semidirect |
| 5. #29507461 | C2 | semidirect |
| 6. #29507460 | C2 | semidirect |
| 7. #459×C241 | C2 | semidirect |
| 53. #14515349 | D8 | semidirect |
| 92. C241 | #1687 | semidirect |
| 96. #459 | D241 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #29508093 | 2 |
| #29507912 | 2 |
| #29507795 | 2 |
| #29507467 | 2 |
| #29507461 | 2 |
| #29507460 | 2 |
| #459×C241 | 2 |
| #1687 | 241 |