Finite Group DatabasebetaFinite Group DatabasebetaOrder 12928.
1004 conjugacy classes of subgroups; only the 485 normal subgroups are shown.
This group has 1004 conjugacy classes of subgroups — too many to draw. Only its 485 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. #20265788 | C2 | direct (N × H) |
| 3. C2×#15692247 | C2 | semidirect |
| 4. C2×#15692245 | C2 | semidirect |
| 6. C2×Q8×Dic101 | C2 | semidirect |
| 8. C2×C4⋊Q8×C101 | C2 | semidirect |
| 11. #15692247 | C22 | semidirect |
| 12. #15692245 | C22 | semidirect |
| 14. Q8×Dic101 | C22 | semidirect |
| 26. C4⋊Q8×C101 | C22 | semidirect |
| 81. C2×C101 | #541 | semidirect |
| 86. C101 | C2×#541 | semidirect |
| 88. C2×C4⋊Q8 | D101 | semidirect |
| 97. C4⋊Q8 | C2×D101 | semidirect |
| 168. C2 | #20265788 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20265788 | 2 |
| C2×#15692250 | 2 |
| C2×#15692247 | 2 |
| C2×#15692245 | 2 |
| C2×#15692231 | 2 |
| C2×Q8×Dic101 | 2 |
| C2×#15692212 | 2 |
| C2×C4⋊Q8×C101 | 2 |
| C2×#541 | 101 |