Finite Group DatabasebetaFinite Group DatabasebetaOrder 12928.
648 conjugacy classes of subgroups; only the 173 normal subgroups are shown.
This group has 648 conjugacy classes of subgroups — too many to draw. Only its 173 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. #20265057 | C2 | semidirect |
| 3. #20265056 | C2 | semidirect |
| 4. #20265055 | C2 | semidirect |
| 5. #20265054 | C2 | semidirect |
| 6. #20265053 | C2 | semidirect |
| 7. #20265053 | C2 | semidirect |
| 8. #20265044 | C2 | semidirect |
| 9. #386×C101 | C2 | semidirect |
| 15. #15692251 | C4 | semidirect |
| 35. C2×D404 | C2×C4 | semidirect |
| 40. C2×C22⋊D101 | C2×C4 | semidirect |
| 41. C2×C22⋊D101 | C2×C4 | semidirect |
| 55. C4×Dic101 | C2×C4 | semidirect |
| 60. C2×D4×C101 | C2×C4 | semidirect |
| 148. C101 | #2380 | semidirect |
| 156. #386 | D101 | semidirect |
| 194. C2×D4 | C4×D101 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15692251 | 2 |
| #20265057 | 2 |
| #20265056 | 2 |
| #20265055 | 2 |
| #20265054 | 2 |
| #20265053 | 2 |
| #20265044 | 2 |
| #386×C101 | 2 |
| #2380 | 101 |