Finite Group DatabasebetaFinite Group DatabasebetaOrder 10624.
136 conjugacy classes of subgroups; only the 47 normal subgroups are shown.
This group has 136 conjugacy classes of subgroups — too many to draw. Only its 47 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. #19128102 | C2 | semidirect |
| 3. #19127528 | C2 | semidirect |
| 4. Dic83⋊C16 | C2 | semidirect |
| 7. #366×C83 | C2 | semidirect |
| 63. C83 | #2228 | semidirect |
| 67. #366 | D83 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19128102 | 2 |
| #19127783 | 2 |
| #19127528 | 2 |
| Dic83⋊C16 | 2 |
| #19127503 | 2 |
| #19127501 | 2 |
| #366×C83 | 2 |
| #2228 | 83 |