Finite Group DatabasebetaFinite Group DatabasebetaOrder 10624.
544 conjugacy classes of subgroups; only the 237 normal subgroups are shown.
This group has 544 conjugacy classes of subgroups — too many to draw. Only its 237 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. C2×Q8×Dic83 | C2 | semidirect |
| 3. #19127802 | C2 | direct (N × H) |
| 4. C2×#14581726 | C2 | semidirect |
| 5. C2×#14581716 | C2 | semidirect |
| 7. C2×#14581702 | C2 | semidirect |
| 12. Q8×Dic83 | C22 | semidirect |
| 21. #14581726 | C22 | semidirect |
| 22. #14581716 | C22 | semidirect |
| 24. #14581702 | C22 | semidirect |
| 27. C2×SD16×C83 | C4 | semidirect |
| 50. C2×Q8×C83 | C2×C4 | semidirect |
| 58. SD16×C83 | C2×C4 | semidirect |
| 59. C2×C8×C83 | C2×C4 | semidirect |
| 68. Q8×C83 | C22×C4 | semidirect |
| 87. C8×C83 | C22×C4 | semidirect |
| 106. C2×C83 | #440 | semidirect |
| 111. C83 | C2×#440 | semidirect |
| 123. C2×SD16 | Dic83 | semidirect |
| 144. C2×Q8 | C2×Dic83 | semidirect |
| 158. SD16 | C2×Dic83 | semidirect |
| 161. C2×C8 | C2×Dic83 | semidirect |
| 179. Q8 | C22×Dic83 | semidirect |
| 199. C8 | C22×Dic83 | semidirect |
| 217. C2 | #19127802 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×Q8×Dic83 | 2 |
| C2×D4×Dic83 | 2 |
| #19127802 | 2 |
| C2×#14581726 | 2 |
| C2×#14581716 | 2 |
| C2×#14581713 | 2 |
| C2×#14581702 | 2 |
| C22×SD16×C83 | 2 |
| C2×#440 | 83 |