Finite Group DatabasebetaFinite Group DatabasebetaOrder 10624.
136 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 136 conjugacy classes of subgroups — too many to draw. Only its 53 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. #19128103 | C2 | semidirect |
| 2. #19127528 | C2 | semidirect |
| 3. #19127526 | C2 | semidirect |
| 4. C4⋊(C83⋊C16) | C2 | semidirect |
| 63. C83 | #2228 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19128103 | 2 |
| #19127528 | 2 |
| #19127526 | 2 |
| C4⋊(C83⋊C16) | 2 |
| #19127502 | 2 |
| C4×D8×C83 | 2 |
| #2228 | 83 |