Finite Group DatabasebetaFinite Group DatabasebetaOrder 10624.
456 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 456 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. #19128249 | C2 | semidirect |
| 2. #19128106 | C2 | semidirect |
| 3. #19128047 | C2 | semidirect |
| 4. #19127934 | C2 | semidirect |
| 5. D8×Dic83 | C2 | semidirect |
| 6. C4×C8×D83 | C2 | semidirect |
| 7. #493×C83 | C2 | semidirect |
| 62. C4×D83 | D8 | semidirect |
| 64. C8×C83 | #41 | semidirect |
| 86. C83 | #3169 | semidirect |
| 89. #493 | D83 | semidirect |
| 151. C8 | #13050589 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19128249 | 2 |
| #19128106 | 2 |
| #19128047 | 2 |
| #19127934 | 2 |
| D8×Dic83 | 2 |
| C4×C8×D83 | 2 |
| #493×C83 | 2 |
| #3169 | 83 |