Finite Group DatabasebetaFinite Group DatabasebetaOrder 10624.
484 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 484 conjugacy classes of subgroups — too many to draw. Only its 133 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×#14581814 | C2 | semidirect |
| 2. #19128356 | C2 | semidirect |
| 3. #19128081 | C2 | semidirect |
| 4. #19127942 | C2 | semidirect |
| 5. #19127907 | C2 | semidirect |
| 6. #19127865 | C2 | semidirect |
| 7. C4×D664 | C2 | semidirect |
| 8. C8×D4×C83 | C2 | semidirect |
| 39. D664 | D4 | semidirect |
| 85. C4×C83 | #135 | semidirect |
| 96. C83 | #3283 | semidirect |
| 104. C8×D4 | D83 | semidirect |
| 183. C4 | #14581814 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#14581814 | 2 |
| #19128356 | 2 |
| #19128081 | 2 |
| #19127942 | 2 |
| #19127907 | 2 |
| #19127865 | 2 |
| C4×D664 | 2 |
| C8×D4×C83 | 2 |
| #3283 | 83 |