Finite Group DatabasebetaFinite Group DatabasebetaOrder 12928.
180 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 180 conjugacy classes of subgroups — too many to draw. Only its 78 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. #20266041 | C2 | semidirect |
| 4. #20266040 | C2 | semidirect |
| 5. #20266039 | C2 | semidirect |
| 6. #20266038 | C2 | semidirect |
| 32. #13108057 | C8 | semidirect |
| 58. C8×C101 | C2×C8 | semidirect |
| 60. #11717579 | C2×C8 | semidirect |
| 78. C101 | #1565 | semidirect |
| 138. C8 | D101⋊C8 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20266196 | 2 |
| D101⋊(C4⋊C8) | 2 |
| #20266041 | 2 |
| #20266040 | 2 |
| #20266039 | 2 |
| #20266038 | 2 |
| #20265129 | 2 |
| #1565 | 101 |