Finite Group DatabasebetaFinite Group DatabasebetaOrder 10624.
384 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 384 conjugacy classes of subgroups — too many to draw. Only its 117 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. #19128436 | C2 | semidirect |
| 2. #19128086 | C2 | semidirect |
| 4. #19127919 | C2 | semidirect |
| 5. #19127901 | C2 | semidirect |
| 6. C8×Dic166 | C2 | semidirect |
| 7. #19127783 | C2 | semidirect |
| 8. C4×Q16×C83 | C2 | semidirect |
| 87. C83 | #3396 | semidirect |
| 94. C4×Q16 | D83 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19128436 | 2 |
| #19128086 | 2 |
| #19128078 | 2 |
| #19127919 | 2 |
| #19127901 | 2 |
| C8×Dic166 | 2 |
| #19127783 | 2 |
| C4×Q16×C83 | 2 |
| #3396 | 83 |