Finite Group DatabasebetaFinite Group DatabasebetaOrder 10624.
604 conjugacy classes of subgroups; only the 173 normal subgroups are shown.
This group has 604 conjugacy classes of subgroups — too many to draw. Only its 173 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×#14581792 | C2 | semidirect |
| 4. #19127628 | C2 | semidirect |
| 5. #19127607 | C2 | semidirect |
| 6. #19127558 | C2 | semidirect |
| 7. C4×C4⋊C4×C83 | C2 | semidirect |
| 84. C4×C83 | #124 | semidirect |
| 94. C83 | #2547 | semidirect |
| 101. C4×C4⋊C4 | D83 | semidirect |
| 180. C4 | #14581780 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#14581792 | 2 |
| C2×#14581780 | 2 |
| C2×C4×D332 | 2 |
| #19127628 | 2 |
| #19127607 | 2 |
| #19127558 | 2 |
| C4×C4⋊C4×C83 | 2 |
| #2547 | 83 |