Finite Group DatabasebetaFinite Group DatabasebetaOrder 10624.
372 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 372 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. #19128424 | C2 | semidirect |
| 2. #19128063 | C2 | semidirect |
| 3. #19128053 | C2 | semidirect |
| 4. #19127993 | C2 | semidirect |
| 5. #19127978 | C2 | semidirect |
| 7. #19127906 | C2 | semidirect |
| 8. #19127832 | C2 | semidirect |
| 9. #19127801 | C2 | semidirect |
| 11. D4×Q8×C83 | C2 | semidirect |
| 123. C83 | #3367 | semidirect |
| 125. D4×Q8 | D83 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19128424 | 2 |
| #19128063 | 2 |
| #19128053 | 2 |
| #19127993 | 2 |
| #19127978 | 2 |
| #19127916 | 2 |
| #19127906 | 2 |
| #19127832 | 2 |
| #19127801 | 2 |
| C4×#13050575 | 2 |
| D4×Q8×C83 | 2 |
| #3367 | 83 |