Finite Group DatabasebetaFinite Group DatabasebetaOrder 10624.
370 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 370 conjugacy classes of subgroups — too many to draw. Only its 141 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. Q8×Dic166 | C2 | semidirect |
| 3. #19128099 | C2 | semidirect |
| 4. #19128098 | C2 | semidirect |
| 7. #19127986 | C2 | semidirect |
| 8. #19127984 | C2 | semidirect |
| 9. C8×Dic166 | C2 | semidirect |
| 64. SD16×C83 | Q8 | semidirect |
| 75. Q8×C83 | C2×Q8 | semidirect |
| 94. Dic166 | SD16 | direct (N × H) |
| 96. C8×C83 | C2×Q8 | semidirect |
| 118. C83 | Q8×SD16 | semidirect |
| 169. SD16 | Dic166 | direct (N × H) |
| 198. Q8 | C2×Dic166 | semidirect |
| 215. C8 | C2×Dic166 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×Dic166 | 2 |
| D4×Dic166 | 2 |
| #19128099 | 2 |
| #19128098 | 2 |
| #19127991 | 2 |
| #19127989 | 2 |
| #19127986 | 2 |
| #19127984 | 2 |
| C8×Dic166 | 2 |
| SD16×Dic83 | 2 |
| C4×SD16×C83 | 2 |
| Q8×SD16 | 83 |