Finite Group DatabasebetaFinite Group DatabasebetaOrder 10624.
374 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 374 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 |
|---|---|---|
| 1. #19128412 | C2 | semidirect |
| 2. #19128366 | C2 | semidirect |
| 3. #19128108 | C2 | semidirect |
| 4. #19128000 | C2 | semidirect |
| 5. #19127990 | C2 | semidirect |
| 6. #19127988 | C2 | semidirect |
| 7. #19127978 | C2 | semidirect |
| 8. #19127831 | C2 | semidirect |
| 11. #498×C83 | C2 | semidirect |
| 50. D664 | Q8 | semidirect |
| 89. D332 | C2×Q8 | semidirect |
| 97. C8×C83 | C2×Q8 | semidirect |
| 122. C83 | #3384 | semidirect |
| 126. #498 | D83 | semidirect |
| 220. C8 | Q8×D83 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19128412 | 2 |
| #19128366 | 2 |
| #19128108 | 2 |
| #19128000 | 2 |
| #19127990 | 2 |
| #19127988 | 2 |
| #19127978 | 2 |
| #19127831 | 2 |
| #19127812 | 2 |
| C4×D664 | 2 |
| #498×C83 | 2 |
| #3384 | 83 |