Finite Group DatabasebetaFinite Group DatabasebetaOrder 12928.
420 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 420 conjugacy classes of subgroups — too many to draw. Only its 141 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. #20265527 | C2 | semidirect |
| 3. #20265505 | C2 | semidirect |
| 4. #20265462 | C2 | semidirect |
| 5. #20265408 | C2 | semidirect |
| 6. #20265379 | C2 | semidirect |
| 7. #20265316 | C2 | semidirect |
| 8. C4×#13108061 | C2 | semidirect |
| 9. D4×#11717579 | C2 | semidirect |
| 10. C2×#15692179 | C2 | semidirect |
| 11. D4×Q8×C101 | C2 | semidirect |
| 83. Q8×C101 | #41 | semidirect |
| 84. D4×C101 | SD16 | semidirect |
| 129. C101 | #3298 | semidirect |
| 130. D4×Q8 | D101 | semidirect |
| 213. Q8 | #13108073 | semidirect |
| 217. D4 | #13108061 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20265831 | 2 |
| #20265527 | 2 |
| #20265505 | 2 |
| #20265462 | 2 |
| #20265408 | 2 |
| #20265379 | 2 |
| #20265316 | 2 |
| C4×#13108061 | 2 |
| D4×#11717579 | 2 |
| C2×#15692179 | 2 |
| D4×Q8×C101 | 2 |
| #3298 | 101 |