Finite Group DatabasebetaFinite Group DatabasebetaOrder 12928.
310 conjugacy classes of subgroups; only the 66 normal subgroups are shown.
This group has 310 conjugacy classes of subgroups — too many to draw. Only its 66 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. #20266256 | C2 | semidirect |
| 2. #20266176 | C2 | semidirect |
| 3. #20266167 | C2 | semidirect |
| 4. #20266152 | C2 | semidirect |
| 5. #20266060 | C2 | semidirect |
| 6. #20266052 | C2 | semidirect |
| 25. #15692286 | C4 | semidirect |
| 26. #15692283 | C4 | semidirect |
| 28. #15692280 | C4 | semidirect |
| 32. #137×C101 | C4 | semidirect |
| 146. C101 | #1881 | semidirect |
| 158. #137 | #87938 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20266256 | 2 |
| #20266176 | 2 |
| #20266167 | 2 |
| #20266152 | 2 |
| #20266060 | 2 |
| #20266052 | 2 |
| #20265976 | 2 |
| #1881 | 101 |