Finite Group DatabasebetaFinite Group DatabasebetaOrder 12928.
424 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 424 conjugacy classes of subgroups — too many to draw. Only its 133 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. #20265490 | C2 | semidirect |
| 3. #20265472 | C2 | semidirect |
| 4. #20265377 | C2 | semidirect |
| 5. #20265316 | C2 | semidirect |
| 6. #20265275 | C2 | semidirect |
| 7. #20265234 | C2 | semidirect |
| 8. C2×C4×Q8×C101 | C2 | semidirect |
| 68. Q8×C101 | #41 | semidirect |
| 112. C101 | #3112 | semidirect |
| 114. C2×C4×Q8 | D101 | semidirect |
| 181. Q8 | #13108074 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20265727 | 2 |
| #20265490 | 2 |
| #20265472 | 2 |
| #20265377 | 2 |
| #20265316 | 2 |
| #20265275 | 2 |
| #20265234 | 2 |
| C2×C4×Q8×C101 | 2 |
| #3112 | 101 |