Finite Group DatabasebetaFinite Group DatabasebetaOrder 10624.
494 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 494 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. #19128372 | C2 | semidirect |
| 3. #19128356 | C2 | semidirect |
| 4. #19128074 | C2 | semidirect |
| 5. #19127930 | C2 | semidirect |
| 6. #19127912 | C2 | semidirect |
| 7. #19127897 | C2 | semidirect |
| 8. #19127865 | C2 | semidirect |
| 9. #19127848 | C2 | semidirect |
| 10. C4×#13050579 | C2 | semidirect |
| 11. C8×D4×C83 | C2 | semidirect |
| 61. #13050579 | D4 | semidirect |
| 127. C4×C83 | #135 | semidirect |
| 141. C83 | #3284 | semidirect |
| 152. C8×D4 | D83 | semidirect |
| 272. 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 |
| #19128372 | 2 |
| #19128356 | 2 |
| #19128074 | 2 |
| #19127930 | 2 |
| #19127912 | 2 |
| #19127897 | 2 |
| #19127865 | 2 |
| #19127848 | 2 |
| C4×#13050579 | 2 |
| C8×D4×C83 | 2 |
| #3284 | 83 |