Finite Group DatabasebetaFinite Group DatabasebetaOrder 10624.
340 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 340 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. #19127683 | C2 | semidirect |
| 4. C2×#14581708 | C2 | semidirect |
| 5. C2×#14581708 | C2 | semidirect |
| 6. #19127471 | C2 | semidirect |
| 7. #344×C83 | C2 | semidirect |
| 45. #13050574 | D4 | semidirect |
| 55. M16×C83 | D4 | semidirect |
| 115. C83 | #1914 | semidirect |
| 122. #344 | D83 | semidirect |
| 166. M16 | D332 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19128467 | 2 |
| #19128270 | 2 |
| #19127683 | 2 |
| C2×#14581708 | 2 |
| #19127471 | 2 |
| #344×C83 | 2 |
| #1914 | 83 |