Finite Group DatabasebetaFinite Group DatabasebetaOrder 10624.
792 conjugacy classes of subgroups; only the 181 normal subgroups are shown.
This group has 792 conjugacy classes of subgroups — too many to draw. Only its 181 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. C23×Dic166 | C2 | semidirect |
| 2. C22×#13050579 | C2 | semidirect |
| 4. #19127842 | C2 | direct (N × H) |
| 5. C2×#14581717 | C2 | semidirect |
| 6. C2×C22⋊C8×C83 | C2 | semidirect |
| 11. C22×Dic166 | C22 | semidirect |
| 16. C2×#13050579 | C22 | semidirect |
| 21. #14581717 | C22 | semidirect |
| 24. C22⋊C8×C83 | C22 | semidirect |
| 32. C2×Dic166 | D4 | semidirect |
| 57. C23×C83 | SD16 | semidirect |
| 82. Dic166 | C2×D4 | semidirect |
| 89. C22×C83 | C2×SD16 | semidirect |
| 102. C2×C83 | #448 | semidirect |
| 108. C83 | C2×#448 | semidirect |
| 114. C2×C22⋊C8 | D83 | semidirect |
| 132. C22⋊C8 | C2×D83 | semidirect |
| 169. C23 | #13050579 | semidirect |
| 201. C22 | C2×#13050579 | semidirect |
| 211. C2 | #19127842 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×Dic166 | 2 |
| C22×#13050579 | 2 |
| C2×#14581766 | 2 |
| #19127842 | 2 |
| C2×#14581717 | 2 |
| C2×C22⋊C8×C83 | 2 |
| C2×#448 | 83 |