Finite Group DatabasebetaFinite Group DatabasebetaOrder 10624.
392 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 392 conjugacy classes of subgroups — too many to draw. Only its 137 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 |
|---|---|---|
| 2. #19127988 | C2 | semidirect |
| 3. #19127986 | C2 | semidirect |
| 4. #19127932 | C2 | semidirect |
| 5. #19127903 | C2 | semidirect |
| 6. #19127901 | C2 | semidirect |
| 7. C2×C4⋊(C83⋊C8) | C2 | semidirect |
| 8. #533×C83 | C2 | semidirect |
| 74. C2×C4×C83 | SD16 | semidirect |
| 113. C83 | #3246 | semidirect |
| 114. #533 | D83 | semidirect |
| 195. C2×C4 | #13050577 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19128251 | 2 |
| #19127988 | 2 |
| #19127986 | 2 |
| #19127932 | 2 |
| #19127903 | 2 |
| #19127901 | 2 |
| C2×C4⋊(C83⋊C8) | 2 |
| #533×C83 | 2 |
| #3246 | 83 |