Finite Group DatabasebetaFinite Group DatabasebetaOrder 10624.
340 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 340 conjugacy classes of subgroups — too many to draw. Only its 137 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 |
|---|---|---|
| 2. #19128111 | C2 | semidirect |
| 3. #19128108 | C2 | semidirect |
| 4. #19128106 | C2 | semidirect |
| 5. #19128105 | C2 | semidirect |
| 6. #19128102 | C2 | semidirect |
| 11. #499×C83 | C2 | semidirect |
| 43. #13050573 | Q8 | semidirect |
| 46. C8×D83 | Q8 | semidirect |
| 108. C83 | #3164 | semidirect |
| 115. #499 | D83 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19128331 | 2 |
| #19128111 | 2 |
| #19128108 | 2 |
| #19128106 | 2 |
| #19128105 | 2 |
| #19128102 | 2 |
| #19127740 | 2 |
| #19127738 | 2 |
| #107×D83 | 2 |
| #19127655 | 2 |
| #499×C83 | 2 |
| #3164 | 83 |