Finite Group DatabasebetaFinite Group DatabasebetaOrder 10624.
476 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 476 conjugacy classes of subgroups — too many to draw. Only its 129 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. C2×#14581824 | C2 | semidirect |
| 2. #19128363 | C2 | semidirect |
| 3. #19128085 | C2 | semidirect |
| 4. #19127948 | C2 | semidirect |
| 5. #19127923 | C2 | semidirect |
| 6. #19127858 | C2 | semidirect |
| 7. #19127849 | C2 | semidirect |
| 8. #19127780 | C2 | semidirect |
| 9. C4×Q16×C83 | C2 | semidirect |
| 64. Q16×C83 | D4 | semidirect |
| 118. C83 | #3277 | semidirect |
| 126. C4×Q16 | D83 | semidirect |
| 170. Q16 | D332 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#14581824 | 2 |
| #19128363 | 2 |
| #19128085 | 2 |
| #19127948 | 2 |
| #19127923 | 2 |
| #19127858 | 2 |
| #19127849 | 2 |
| #19127780 | 2 |
| C4×Q16×C83 | 2 |
| #3277 | 83 |