Finite Group DatabasebetaFinite Group DatabasebetaOrder 10624.
484 conjugacy classes of subgroups; only the 153 normal subgroups are shown.
This group has 484 conjugacy classes of subgroups — too many to draw. Only its 153 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. C2×#14581823 | C2 | semidirect |
| 3. #19127923 | C2 | semidirect |
| 4. #19127911 | C2 | semidirect |
| 5. #19127901 | C2 | semidirect |
| 6. #19127725 | C2 | semidirect |
| 7. #19127700 | C2 | semidirect |
| 8. C2×C4×Q8×C83 | C2 | semidirect |
| 52. C2×Q8×C83 | D4 | semidirect |
| 111. C4×C83 | #137 | semidirect |
| 121. C83 | #3037 | semidirect |
| 124. C2×C4×Q8 | D83 | semidirect |
| 160. C2×Q8 | D332 | semidirect |
| 233. C4 | #14581823 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#14581823 | 2 |
| #19128251 | 2 |
| #19127923 | 2 |
| #19127911 | 2 |
| #19127901 | 2 |
| #19127725 | 2 |
| #19127700 | 2 |
| C2×C4×Q8×C83 | 2 |
| #3037 | 83 |