Finite Group DatabasebetaFinite Group DatabasebetaOrder 12928.
704 conjugacy classes of subgroups; only the 237 normal subgroups are shown.
This group has 704 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 |
|---|---|---|
| 3. #20265075 | C2 | semidirect |
| 4. #20265048 | C2 | semidirect |
| 5. #20265043 | C2 | semidirect |
| 6. #20265036 | C2 | semidirect |
| 7. #95×D101 | C2 | semidirect |
| 8. C4×C4⋊C4×C101 | C2 | semidirect |
| 13. C4×D404 | C4 | semidirect |
| 37. C2×C4×D101 | C2×C4 | semidirect |
| 39. C4⋊Dic101 | C2×C4 | semidirect |
| 42. #13108051 | C2×C4 | semidirect |
| 50. C42×C101 | C2×C4 | semidirect |
| 75. D404 | C4⋊C4 | semidirect |
| 102. C101 | #2349 | semidirect |
| 109. C4×C4⋊C4 | D101 | semidirect |
| 152. C42 | C4×D101 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×D404 | 2 |
| #20265075 | 2 |
| #20265048 | 2 |
| #20265043 | 2 |
| #20265036 | 2 |
| #95×D101 | 2 |
| C4×C4⋊C4×C101 | 2 |
| #2349 | 101 |