Finite Group DatabasebetaFinite Group DatabasebetaOrder 10624.
386 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 386 conjugacy classes of subgroups — too many to draw. Only its 115 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. #19128417 | C2 | semidirect |
| 2. #19128356 | C2 | semidirect |
| 3. #19128097 | C2 | semidirect |
| 4. #19128023 | C2 | semidirect |
| 5. #19128021 | C2 | semidirect |
| 6. #19127982 | C2 | semidirect |
| 7. #19127953 | C2 | semidirect |
| 8. C4×#13050575 | C2 | semidirect |
| 9. #19127778 | C2 | semidirect |
| 10. #19127740 | C2 | semidirect |
| 11. #476×C83 | C2 | semidirect |
| 101. C83⋊C8 | #41 | semidirect |
| 128. C83 | #3354 | semidirect |
| 134. #476 | D83 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19128417 | 2 |
| #19128356 | 2 |
| #19128097 | 2 |
| #19128023 | 2 |
| #19128021 | 2 |
| #19127982 | 2 |
| #19127953 | 2 |
| C4×#13050575 | 2 |
| #19127778 | 2 |
| #19127740 | 2 |
| #476×C83 | 2 |
| #3354 | 83 |