Finite Group DatabasebetaFinite Group DatabasebetaOrder 10624.
908 conjugacy classes of subgroups; only the 285 normal subgroups are shown.
This group has 908 conjugacy classes of subgroups — too many to draw. Only its 285 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 |
|---|---|---|
| 4. #19127622 | C2 | direct (N × H) |
| 31. C22×Dic83 | Q8 | semidirect |
| 42. C22×C4×C83 | Q8 | semidirect |
| 57. C2×C4×C83 | C2×Q8 | semidirect |
| 68. C2×Dic83 | C2×Q8 | semidirect |
| 85. C2×C83 | #395 | semidirect |
| 92. C83 | C2×#395 | semidirect |
| 131. C22×C4 | Dic166 | semidirect |
| 161. C2×C4 | C2×Dic166 | semidirect |
| 177. C2 | #19127622 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×Dic166 | 2 |
| C22×C4⋊Dic83 | 2 |
| C22×Dic83⋊C4 | 2 |
| #19127622 | 2 |
| C2×C83⋊#95 | 2 |
| C2×#95×C83 | 2 |
| C2×#395 | 83 |