Finite Group DatabasebetaFinite Group DatabasebetaOrder 10624.
356 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 356 conjugacy classes of subgroups — too many to draw. Only its 125 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. #19128105 | C2 | semidirect |
| 3. #19128038 | C2 | semidirect |
| 4. #19128036 | C2 | semidirect |
| 5. #19127995 | C2 | semidirect |
| 6. #19127943 | C2 | semidirect |
| 7. #19127942 | C2 | semidirect |
| 8. #19127795 | C2 | semidirect |
| 10. #107×D83 | C2 | semidirect |
| 11. C2×#107×C83 | C2 | semidirect |
| 78. C22⋊D83 | Q16 | semidirect |
| 117. C83 | #3338 | semidirect |
| 128. C2×#107 | D83 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19128406 | 2 |
| #19128105 | 2 |
| #19128038 | 2 |
| #19128036 | 2 |
| #19127995 | 2 |
| #19127943 | 2 |
| #19127942 | 2 |
| #19127795 | 2 |
| C8×C22⋊D83 | 2 |
| #107×D83 | 2 |
| C2×#107×C83 | 2 |
| #3338 | 83 |