Finite Group DatabasebetaFinite Group DatabasebetaOrder 10624.
484 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 484 conjugacy classes of subgroups — too many to draw. Only its 145 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. C2×#14581822 | C2 | semidirect |
| 2. C2×C4×Dic166 | C2 | semidirect |
| 3. #19127920 | C2 | semidirect |
| 4. #19127908 | C2 | semidirect |
| 5. #19127898 | C2 | semidirect |
| 6. #19127725 | C2 | semidirect |
| 7. #19127702 | C2 | semidirect |
| 36. C2×Dic166 | D4 | semidirect |
| 110. C4×C83 | #137 | semidirect |
| 121. C83 | #3037 | semidirect |
| 233. C4 | #14581822 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#14581822 | 2 |
| C2×C4×Dic166 | 2 |
| #19127920 | 2 |
| #19127908 | 2 |
| #19127898 | 2 |
| #19127725 | 2 |
| #19127702 | 2 |
| #532×C83 | 2 |
| #3037 | 83 |