Finite Group DatabasebetaFinite Group DatabasebetaOrder 12928.
494 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 494 conjugacy classes of subgroups — too many to draw. Only its 125 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. #20265847 | C2 | semidirect |
| 3. #20265831 | C2 | semidirect |
| 4. #20265549 | C2 | semidirect |
| 5. #20265405 | C2 | semidirect |
| 6. #20265388 | C2 | semidirect |
| 7. #20265340 | C2 | semidirect |
| 8. #20265319 | C2 | semidirect |
| 9. C4×#13108062 | C2 | semidirect |
| 10. #20265242 | C2 | semidirect |
| 11. #459×C101 | C2 | semidirect |
| 58. #13108062 | D4 | semidirect |
| 127. C4×C101 | #135 | semidirect |
| 141. C101 | #3284 | semidirect |
| 148. #459 | D101 | semidirect |
| 272. 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 |
| #20265847 | 2 |
| #20265831 | 2 |
| #20265549 | 2 |
| #20265405 | 2 |
| #20265388 | 2 |
| #20265340 | 2 |
| #20265319 | 2 |
| C4×#13108062 | 2 |
| #20265242 | 2 |
| #459×C101 | 2 |
| #3284 | 101 |