Finite Group DatabasebetaFinite Group DatabasebetaOrder 10624.
386 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 386 conjugacy classes of subgroups — too many to draw. Only its 117 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. #19128354 | C2 | semidirect |
| 3. #19128027 | C2 | semidirect |
| 4. #19128021 | C2 | semidirect |
| 5. #19127988 | C2 | semidirect |
| 6. #19127978 | C2 | semidirect |
| 7. #19127955 | C2 | semidirect |
| 8. C4×D664 | C2 | semidirect |
| 9. #19127780 | C2 | semidirect |
| 10. #19127740 | C2 | semidirect |
| 11. #498×C83 | C2 | semidirect |
| 100. C8×C83 | #41 | semidirect |
| 128. C83 | #3354 | semidirect |
| 131. #498 | D83 | semidirect |
| 229. C8 | #13050591 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19128417 | 2 |
| #19128354 | 2 |
| #19128027 | 2 |
| #19128021 | 2 |
| #19127988 | 2 |
| #19127978 | 2 |
| #19127955 | 2 |
| C4×D664 | 2 |
| #19127780 | 2 |
| #19127740 | 2 |
| #498×C83 | 2 |
| #3354 | 83 |