Finite Group DatabasebetaFinite Group DatabasebetaOrder 10624.
404 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 404 conjugacy classes of subgroups — too many to draw. Only its 149 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×D332 | C2 | semidirect |
| 2. #19128104 | C2 | semidirect |
| 3. #19127981 | C2 | semidirect |
| 4. #19127978 | C2 | semidirect |
| 5. Q8×C83⋊C8 | C2 | semidirect |
| 7. D4×Q8×C83 | C2 | semidirect |
| 28. #13050575 | Q8 | direct (N × H) |
| 47. Q8×C83 | D8 | semidirect |
| 49. D4×C83 | C2×Q8 | semidirect |
| 57. D332 | C2×Q8 | semidirect |
| 61. C83⋊C8 | C2×Q8 | semidirect |
| 81. C83 | Q8×D8 | semidirect |
| 83. D4×Q8 | D83 | semidirect |
| 129. Q8 | #13050575 | direct (N × H) |
| 133. D4 | Q8×D83 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×D332 | 2 |
| #19128104 | 2 |
| #19127981 | 2 |
| #19127978 | 2 |
| Q8×C83⋊C8 | 2 |
| C4×#13050575 | 2 |
| D4×Q8×C83 | 2 |
| Q8×D8 | 83 |