Finite Group DatabasebetaFinite Group DatabasebetaOrder 10624.
174 conjugacy classes of subgroups; only the 49 normal subgroups are shown.
This group has 174 conjugacy classes of subgroups — too many to draw. Only its 49 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×#14581737 | C2 | semidirect |
| 2. C2×#14581736 | C2 | semidirect |
| 4. #19127795 | C2 | semidirect |
| 5. Dic83⋊C16 | C2 | semidirect |
| 6. #19127501 | C2 | semidirect |
| 7. #357×C83 | C2 | semidirect |
| 26. Dic332 | D4 | semidirect |
| 71. Dic83 | SD32 | semidirect |
| 78. C83 | #2207 | semidirect |
| 85. #357 | D83 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#14581737 | 2 |
| C2×#14581736 | 2 |
| #19128076 | 2 |
| #19127795 | 2 |
| Dic83⋊C16 | 2 |
| #19127501 | 2 |
| #357×C83 | 2 |
| #2207 | 83 |