Finite Group DatabasebetaFinite Group DatabasebetaOrder 10624.
472 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 472 conjugacy classes of subgroups — too many to draw. Only its 149 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. C22×#13050580 | C2 | semidirect |
| 3. #19128080 | C2 | semidirect |
| 4. #19127940 | C2 | semidirect |
| 5. #19127911 | C2 | semidirect |
| 6. #19127908 | C2 | semidirect |
| 7. #19127857 | C2 | semidirect |
| 8. #19127856 | C2 | semidirect |
| 9. C4×#13050580 | C2 | semidirect |
| 52. #13050580 | D4 | direct (N × H) |
| 88. D4×C83 | Q16 | semidirect |
| 113. C22×C83 | C2×Q16 | semidirect |
| 120. C4×C83 | C2×Q16 | semidirect |
| 131. C83 | D4×Q16 | semidirect |
| 224. D4 | #13050580 | direct (N × H) |
| 244. C22 | C2×#13050580 | semidirect |
| 254. C4 | C2×#13050580 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#13050580 | 2 |
| D4×Dic166 | 2 |
| #19128080 | 2 |
| #19127940 | 2 |
| #19127911 | 2 |
| #19127908 | 2 |
| #19127857 | 2 |
| #19127856 | 2 |
| C4×#13050580 | 2 |
| D4×C83⋊C8 | 2 |
| D4×Q8×C83 | 2 |
| D4×Q16 | 83 |