Finite Group DatabasebetaFinite Group DatabasebetaOrder 10624.
552 conjugacy classes of subgroups; only the 181 normal subgroups are shown.
This group has 552 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 |
|---|---|---|
| 4. #19128079 | C2 | direct (N × H) |
| 56. C2×Dic83 | Q16 | semidirect |
| 71. Dic83 | C2×Q16 | semidirect |
| 72. C2×C83 | #494 | semidirect |
| 76. C83 | C2×#494 | semidirect |
| 148. C2 | #19128079 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×Dic332 | 2 |
| C22×#13050580 | 2 |
| C2×#14581790 | 2 |
| #19128079 | 2 |
| C2×C8×Dic83 | 2 |
| C22×Q16×C83 | 2 |
| C2×#494 | 83 |