Finite Group DatabasebetaFinite Group DatabasebetaOrder 10624.
380 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 380 conjugacy classes of subgroups — too many to draw. Only its 141 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 |
|---|---|---|
| 3. #19128070 | C2 | semidirect |
| 4. #19128052 | C2 | semidirect |
| 68. C83 | #3139 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19128258 | 2 |
| C2×#14581792 | 2 |
| #19128070 | 2 |
| #19128052 | 2 |
| #19127711 | 2 |
| C4×M16×C83 | 2 |
| #3139 | 83 |