Finite Group DatabasebetaFinite Group DatabasebetaOrder 10624.
392 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 392 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. #19128258 | C2 | semidirect |
| 3. #19128070 | C2 | semidirect |
| 4. #19128066 | C2 | semidirect |
| 5. #19128061 | C2 | semidirect |
| 6. #19127698 | C2 | semidirect |
| 7. C2×#97×C83 | C2 | semidirect |
| 79. C83 | #3135 | semidirect |
| 86. C2×#97 | D83 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19128258 | 2 |
| #19128251 | 2 |
| #19128070 | 2 |
| #19128066 | 2 |
| #19128061 | 2 |
| #19127698 | 2 |
| C2×#97×C83 | 2 |
| #3135 | 83 |