Finite Group DatabasebetaFinite Group DatabasebetaOrder 10624.
380 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 380 conjugacy classes of subgroups — too many to draw. Only its 145 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 |
|---|---|---|
| 3. #19128108 | C2 | semidirect |
| 4. #19128106 | C2 | semidirect |
| 5. #19128104 | C2 | semidirect |
| 6. #19128097 | C2 | semidirect |
| 9. #498×C83 | C2 | semidirect |
| 43. #13050573 | Q8 | semidirect |
| 86. C8×C83 | C2×Q8 | semidirect |
| 87. C83⋊C8 | C2×Q8 | semidirect |
| 107. C83 | #3165 | semidirect |
| 114. #498 | D83 | semidirect |
| 194. C8 | Q8×D83 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19128256 | 2 |
| C4⋊Q8×D83 | 2 |
| #19128108 | 2 |
| #19128106 | 2 |
| #19128104 | 2 |
| #19128097 | 2 |
| #19127740 | 2 |
| C4×#13050573 | 2 |
| #498×C83 | 2 |
| #3165 | 83 |