Finite Group DatabasebetaFinite Group DatabasebetaOrder 10624.
340 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 340 conjugacy classes of subgroups — too many to draw. Only its 105 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 |
|---|---|---|
| 2. C2×#14581715 | C2 | semidirect |
| 4. C2×#14581702 | C2 | semidirect |
| 5. #19127606 | C2 | semidirect |
| 7. C2×#107×C83 | C2 | semidirect |
| 12. C2×#13050579 | C4 | semidirect |
| 86. C8×C83 | C22⋊C4 | semidirect |
| 113. C83 | #1973 | semidirect |
| 115. C2×#107 | D83 | semidirect |
| 200. C8 | (C2×D83)⋊C4 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#13050579 | 2 |
| C2×#14581715 | 2 |
| C2×#14581712 | 2 |
| C2×#14581702 | 2 |
| #19127606 | 2 |
| #19127602 | 2 |
| C2×#107×C83 | 2 |
| #1973 | 83 |