Finite Group DatabasebetaFinite Group DatabasebetaOrder 28736.
148 conjugacy classes of subgroups; only the 45 normal subgroups are shown.
This group has 148 conjugacy classes of subgroups — too many to draw. Only its 45 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. C2×Dic1796 | C2 | semidirect |
| 3. C2×#20297726 | C2 | semidirect |
| 5. #28385263 | C2 | semidirect |
| 7. #103×C449 | C2 | semidirect |
| 45. C2×D449 | Q16 | semidirect |
| 57. C449 | #451 | semidirect |
| 64. #103 | D449 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×Q8×D449 | 2 |
| C2×Dic1796 | 2 |
| C2×#20297726 | 2 |
| #28385320 | 2 |
| #28385263 | 2 |
| #28385252 | 2 |
| #103×C449 | 2 |
| #451 | 449 |