Finite Group DatabasebetaFinite Group DatabasebetaOrder 10624.
344 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 344 conjugacy classes of subgroups — too many to draw. Only its 79 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. #19128467 | C2 | semidirect |
| 3. #19127706 | C2 | semidirect |
| 4. #19127674 | C2 | semidirect |
| 5. #19127458 | C2 | semidirect |
| 6. #19127457 | C2 | semidirect |
| 7. #418×C83 | C2 | semidirect |
| 13. #14581788 | C4 | semidirect |
| 14. #14581779 | C4 | semidirect |
| 37. C2×C83⋊C8 | D4 | semidirect |
| 56. C2×C8×C83 | D4 | semidirect |
| 116. C83 | #1910 | semidirect |
| 120. #418 | D83 | semidirect |
| 165. C2×C8 | C22⋊D83 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19128467 | 2 |
| #19128268 | 2 |
| #19127706 | 2 |
| #19127674 | 2 |
| #19127458 | 2 |
| #19127457 | 2 |
| #418×C83 | 2 |
| #1910 | 83 |