Finite Group DatabasebetaFinite Group DatabasebetaOrder 10624.
302 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 302 conjugacy classes of subgroups — too many to draw. Only its 93 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. #19127744 | C2 | semidirect |
| 4. #19127570 | C2 | semidirect |
| 5. #19127470 | C2 | semidirect |
| 6. #19127460 | C2 | semidirect |
| 15. #14581719 | C4 | semidirect |
| 31. #13050574 | C2×C4 | semidirect |
| 38. C4×Dic83 | C2×C4 | semidirect |
| 62. Q8×C83 | C4⋊C4 | semidirect |
| 66. D4×C83 | C4⋊C4 | semidirect |
| 113. C83 | #1859 | semidirect |
| 175. Q8 | Dic83⋊C4 | semidirect |
| 179. D4 | Dic83⋊C4 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19127744 | 2 |
| C2×#14581719 | 2 |
| #19127702 | 2 |
| #19127570 | 2 |
| #19127470 | 2 |
| #19127460 | 2 |
| #520×C83 | 2 |
| #1859 | 83 |