Finite Group DatabasebetaFinite Group DatabasebetaOrder 12928.
496 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 496 conjugacy classes of subgroups — too many to draw. Only its 131 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. C2×#15692274 | C2 | semidirect |
| 2. #20265725 | C2 | semidirect |
| 3. C4×#13108073 | C2 | semidirect |
| 4. #20265398 | C2 | semidirect |
| 5. #20265390 | C2 | semidirect |
| 6. #20265388 | C2 | semidirect |
| 7. #20265382 | C2 | semidirect |
| 8. #20265374 | C2 | semidirect |
| 9. C4⋊C8×D101 | C2 | semidirect |
| 10. #20265170 | C2 | semidirect |
| 11. #459×C101 | C2 | semidirect |
| 47. #13108073 | D4 | semidirect |
| 135. C4×C101 | #135 | semidirect |
| 151. C101 | #3035 | semidirect |
| 160. #459 | D101 | semidirect |
| 292. C4 | #15692274 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15692274 | 2 |
| #20265725 | 2 |
| C4×#13108073 | 2 |
| #20265398 | 2 |
| #20265390 | 2 |
| #20265388 | 2 |
| #20265382 | 2 |
| #20265374 | 2 |
| C4⋊C8×D101 | 2 |
| #20265170 | 2 |
| #459×C101 | 2 |
| #3035 | 101 |