Finite Group DatabasebetaFinite Group DatabasebetaOrder 10624.
446 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 446 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. #19128251 | C2 | semidirect |
| 2. #19128099 | C2 | semidirect |
| 3. #19128078 | C2 | semidirect |
| 4. #19128048 | C2 | semidirect |
| 5. #19127954 | C2 | semidirect |
| 6. #19127814 | C2 | semidirect |
| 7. C4×M16×C83 | C2 | semidirect |
| 60. C8×C83 | #41 | semidirect |
| 77. C83 | #3184 | semidirect |
| 84. C4×M16 | D83 | semidirect |
| 137. C8 | #13050590 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19128251 | 2 |
| #19128099 | 2 |
| #19128078 | 2 |
| #19128048 | 2 |
| #19127954 | 2 |
| #19127814 | 2 |
| C4×M16×C83 | 2 |
| #3184 | 83 |