Finite Group DatabasebetaFinite Group DatabasebetaOrder 10624.
154 conjugacy classes of subgroups; only the 47 normal subgroups are shown.
This group has 154 conjugacy classes of subgroups — too many to draw. Only its 47 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. #19128144 | C2 | semidirect |
| 3. #19128085 | C2 | semidirect |
| 4. #19127819 | C2 | semidirect |
| 5. #19127518 | C2 | semidirect |
| 6. #19127515 | C2 | semidirect |
| 7. #364×C83 | C2 | semidirect |
| 75. C83 | #2212 | semidirect |
| 80. #364 | D83 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19128144 | 2 |
| #19128139 | 2 |
| #19128085 | 2 |
| #19127819 | 2 |
| #19127518 | 2 |
| #19127515 | 2 |
| #364×C83 | 2 |
| #2212 | 83 |