Finite Group DatabasebetaFinite Group DatabasebetaOrder 10624.
382 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 382 conjugacy classes of subgroups — too many to draw. Only its 73 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. #19128275 | C2 | semidirect |
| 3. C2×#14581781 | C2 | semidirect |
| 4. C2×#14581718 | C2 | semidirect |
| 5. #19127707 | C2 | semidirect |
| 6. #19127462 | C2 | semidirect |
| 7. C2×#101×C83 | C2 | semidirect |
| 131. C83 | #2003 | semidirect |
| 137. C2×#101 | D83 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#14581820 | 2 |
| #19128275 | 2 |
| C2×#14581781 | 2 |
| C2×#14581718 | 2 |
| #19127707 | 2 |
| #19127462 | 2 |
| C2×#101×C83 | 2 |
| #2003 | 83 |