Finite Group DatabasebetaFinite Group DatabasebetaOrder 10624.
164 conjugacy classes of subgroups; only the 49 normal subgroups are shown.
This group has 164 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×#14581736 | C2 | semidirect |
| 2. C2×C16×D83 | C2 | semidirect |
| 3. #19127943 | C2 | semidirect |
| 5. #19127528 | C2 | semidirect |
| 6. #19127506 | C2 | semidirect |
| 7. #357×C83 | C2 | semidirect |
| 33. C83⋊C16 | D4 | semidirect |
| 63. C2×D83 | SD32 | semidirect |
| 76. C83 | #2217 | semidirect |
| 83. #357 | D83 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#14581736 | 2 |
| C2×C16×D83 | 2 |
| #19127943 | 2 |
| #19127934 | 2 |
| #19127528 | 2 |
| #19127506 | 2 |
| #357×C83 | 2 |
| #2217 | 83 |