Finite Group DatabasebetaFinite Group DatabasebetaOrder 4864.
654 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 654 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. #14573734 | C2 | semidirect |
| 3. #14564578 | C2 | semidirect |
| 4. #14562233 | C2 | semidirect |
| 5. #14562078 | C2 | semidirect |
| 6. #14561491 | C2 | semidirect |
| 66. #10597315 | D4 | semidirect |
| 67. #10597315 | D4 | semidirect |
| 79. C4⋊(C19⋊C8) | D4 | semidirect |
| 82. #10597260 | D4 | semidirect |
| 311. C19 | #10008 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14574638 | 2 |
| #14573734 | 2 |
| #14564578 | 2 |
| #14562233 | 2 |
| #14562078 | 2 |
| #14561491 | 2 |
| C19×#2540 | 2 |
| #10008 | 19 |