Finite Group DatabasebetaFinite Group DatabasebetaOrder 10624.
360 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 360 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. #19128429 | C2 | semidirect |
| 3. #19128110 | C2 | semidirect |
| 4. #19128106 | C2 | semidirect |
| 6. #19127997 | C2 | semidirect |
| 7. #19127987 | C2 | semidirect |
| 11. #446×C83 | C2 | semidirect |
| 49. #13050579 | Q8 | semidirect |
| 93. Dic166 | C2×Q8 | semidirect |
| 96. C8×C83 | C2×Q8 | semidirect |
| 117. C83 | #3386 | semidirect |
| 126. #446 | D83 | semidirect |
| 213. C8 | Q8×D83 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19128429 | 2 |
| Q8×D332 | 2 |
| #19128110 | 2 |
| #19128106 | 2 |
| #19128002 | 2 |
| #19127997 | 2 |
| #19127987 | 2 |
| #19127982 | 2 |
| #19127803 | 2 |
| C4×#13050579 | 2 |
| #446×C83 | 2 |
| #3386 | 83 |