Finite Group DatabasebetaFinite Group DatabasebetaOrder 10624.
338 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 338 conjugacy classes of subgroups — too many to draw. Only its 133 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. #19128430 | C2 | semidirect |
| 3. #19128101 | C2 | semidirect |
| 4. #19128099 | C2 | semidirect |
| 5. #19128006 | C2 | semidirect |
| 7. #19127996 | C2 | semidirect |
| 9. C8×Dic166 | C2 | semidirect |
| 63. SD16×C83 | Q8 | semidirect |
| 115. C83 | #3381 | semidirect |
| 163. SD16 | Dic166 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19128430 | 2 |
| #19128408 | 2 |
| #19128101 | 2 |
| #19128099 | 2 |
| #19128006 | 2 |
| #19128003 | 2 |
| #19127996 | 2 |
| #19127981 | 2 |
| C8×Dic166 | 2 |
| SD16×Dic83 | 2 |
| C4×SD16×C83 | 2 |
| #3381 | 83 |