Finite Group DatabasebetaFinite Group DatabasebetaOrder 10624.
552 conjugacy classes of subgroups; only the 157 normal subgroups are shown.
This group has 552 conjugacy classes of subgroups — too many to draw. Only its 157 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×#14581823 | C2 | semidirect |
| 3. #19128093 | C2 | semidirect |
| 4. #19128080 | C2 | semidirect |
| 5. #19128075 | C2 | semidirect |
| 6. C4×#13050574 | C2 | semidirect |
| 7. C2×C4⋊Q8×C83 | C2 | semidirect |
| 34. #13050574 | D4 | semidirect |
| 76. C4×C83 | #137 | semidirect |
| 84. C83 | #3152 | semidirect |
| 87. C2×C4⋊Q8 | D83 | semidirect |
| 161. C4 | #14581823 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#14581823 | 2 |
| #19128251 | 2 |
| #19128093 | 2 |
| #19128080 | 2 |
| #19128075 | 2 |
| C4×#13050574 | 2 |
| C2×C4⋊Q8×C83 | 2 |
| #3152 | 83 |