Finite Group DatabasebetaFinite Group DatabasebetaOrder 12928.
656 conjugacy classes of subgroups; only the 157 normal subgroups are shown.
This group has 656 conjugacy classes of subgroups — too many to draw. Only its 157 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×#15692281 | C2 | semidirect |
| 2. #20265727 | C2 | semidirect |
| 3. #20265564 | C2 | semidirect |
| 4. #20265553 | C2 | semidirect |
| 5. #20265549 | C2 | semidirect |
| 6. C4×#13108058 | C2 | semidirect |
| 7. C2×#127×C101 | C2 | semidirect |
| 10. C2×#13108062 | C22 | semidirect |
| 11. C2×#13108059 | C22 | semidirect |
| 13. #15692255 | C22 | semidirect |
| 14. #15692252 | C22 | semidirect |
| 15. #15692243 | C22 | semidirect |
| 18. #15692166 | C22 | semidirect |
| 19. C4×#11717579 | C22 | semidirect |
| 34. #13108058 | D4 | semidirect |
| 71. #11717579 | C2×D4 | semidirect |
| 82. C4×C101 | AGL(1,ℤ/8) | semidirect |
| 91. C101 | #3151 | semidirect |
| 94. C2×#127 | D101 | semidirect |
| 174. C4 | #15692281 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15692281 | 2 |
| #20265727 | 2 |
| #20265564 | 2 |
| #20265553 | 2 |
| #20265549 | 2 |
| C4×#13108058 | 2 |
| C2×#127×C101 | 2 |
| #3151 | 101 |