Finite Group DatabasebetaFinite Group DatabasebetaOrder 10624.
394 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 394 conjugacy classes of subgroups — too many to draw. Only its 75 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. C2×#14581822 | C2 | semidirect |
| 2. C2×#14581779 | C2 | semidirect |
| 3. C2×#14581719 | C2 | semidirect |
| 4. #19127709 | C2 | semidirect |
| 5. C2×#14581709 | C2 | semidirect |
| 6. #19127460 | C2 | semidirect |
| 34. C2×Dic166 | D4 | semidirect |
| 42. #13050574 | D4 | semidirect |
| 47. C4×Dic83 | D4 | semidirect |
| 132. C83 | #2004 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#14581822 | 2 |
| C2×#14581779 | 2 |
| C2×#14581719 | 2 |
| #19127709 | 2 |
| C2×#14581709 | 2 |
| #19127460 | 2 |
| #535×C83 | 2 |
| #2004 | 83 |