Finite Group DatabasebetaFinite Group DatabasebetaOrder 4864.
684 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 684 conjugacy classes of subgroups — too many to draw. Only its 85 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. #14574638 | C2 | semidirect |
| 2. #14574009 | C2 | semidirect |
| 3. #14562349 | C2 | semidirect |
| 4. #14562233 | C2 | semidirect |
| 5. #14562146 | C2 | semidirect |
| 6. #14561528 | C2 | semidirect |
| 59. #10597315 | D4 | semidirect |
| 60. #10597315 | D4 | semidirect |
| 72. C4⋊(C19⋊C8) | D4 | semidirect |
| 75. #10597260 | D4 | semidirect |
| 277. C19 | #10096 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14574638 | 2 |
| #14574009 | 2 |
| #14562349 | 2 |
| #14562233 | 2 |
| #14562146 | 2 |
| #14561528 | 2 |
| C19×#2657 | 2 |
| #10096 | 19 |