Finite Group DatabasebetaFinite Group DatabasebetaOrder 10624.
456 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 456 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. #19128248 | C2 | semidirect |
| 2. #19128105 | C2 | semidirect |
| 3. #19128076 | C2 | semidirect |
| 4. #19128046 | C2 | semidirect |
| 5. #19127938 | C2 | semidirect |
| 6. #19127936 | C2 | semidirect |
| 7. #19127934 | C2 | semidirect |
| 8. C4×D664 | C2 | semidirect |
| 9. C4×#13050575 | C2 | semidirect |
| 10. C4×C8×D83 | C2 | semidirect |
| 11. C4×D8×C83 | C2 | semidirect |
| 96. C4×D83 | D8 | semidirect |
| 99. C8×C83 | #41 | semidirect |
| 101. C83⋊C8 | #41 | semidirect |
| 128. C83 | #3169 | semidirect |
| 138. C4×D8 | D83 | semidirect |
| 229. C8 | #13050590 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19128248 | 2 |
| #19128105 | 2 |
| #19128076 | 2 |
| #19128046 | 2 |
| #19127938 | 2 |
| #19127936 | 2 |
| #19127934 | 2 |
| C4×D664 | 2 |
| C4×#13050575 | 2 |
| C4×C8×D83 | 2 |
| C4×D8×C83 | 2 |
| #3169 | 83 |