Finite Group DatabasebetaFinite Group DatabasebetaOrder 10624.
374 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 374 conjugacy classes of subgroups — too many to draw. Only its 133 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. #19128408 | C2 | semidirect |
| 2. D4×Dic166 | C2 | semidirect |
| 3. #19128109 | C2 | semidirect |
| 4. #19128099 | C2 | semidirect |
| 5. #19128003 | C2 | semidirect |
| 6. #19127991 | C2 | semidirect |
| 7. #19127989 | C2 | semidirect |
| 8. #19127981 | C2 | semidirect |
| 9. #19127831 | C2 | semidirect |
| 65. D8×C83 | Q8 | semidirect |
| 78. D4×C83 | C2×Q8 | semidirect |
| 97. C8×C83 | C2×Q8 | semidirect |
| 122. C83 | #3384 | semidirect |
| 174. D8 | Dic166 | semidirect |
| 204. D4 | C2×Dic166 | semidirect |
| 220. C8 | C2×Dic166 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19128408 | 2 |
| D4×Dic166 | 2 |
| #19128109 | 2 |
| #19128099 | 2 |
| #19128003 | 2 |
| #19127991 | 2 |
| #19127989 | 2 |
| #19127981 | 2 |
| #19127831 | 2 |
| #19127813 | 2 |
| C4×D8×C83 | 2 |
| #3384 | 83 |