Finite Group DatabasebetaFinite Group DatabasebetaOrder 12928.
548 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 548 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×#15692279 | C2 | semidirect |
| 2. #20265725 | C2 | semidirect |
| 3. C4×D4×D101 | C2 | semidirect |
| 4. #20265391 | C2 | semidirect |
| 5. #20265390 | C2 | semidirect |
| 6. #20265383 | C2 | semidirect |
| 7. #20265382 | C2 | semidirect |
| 8. #20265369 | C2 | semidirect |
| 9. #20265199 | C2 | semidirect |
| 10. #20265175 | C2 | semidirect |
| 11. #459×C101 | C2 | semidirect |
| 20. #15692255 | C22 | semidirect |
| 21. #15692242 | C22 | semidirect |
| 34. C4⋊#11717579 | C22 | semidirect |
| 35. #15692184 | C22 | semidirect |
| 36. #15692180 | C22 | semidirect |
| 37. #15692178 | C22 | semidirect |
| 38. #15692176 | C22 | semidirect |
| 40. #127×C101 | C22 | semidirect |
| 42. C4⋊C8×C101 | C22 | semidirect |
| 43. #102×C101 | C22 | semidirect |
| 52. D4×D101 | D4 | semidirect |
| 145. C4×C101 | AGL(1,ℤ/8) | semidirect |
| 161. C101 | #3036 | semidirect |
| 170. #459 | D101 | semidirect |
| 183. #127 | C2×D101 | semidirect |
| 200. C4⋊C8 | C2×D101 | semidirect |
| 204. #102 | C2×D101 | semidirect |
| 311. C4 | #15692279 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15692279 | 2 |
| #20265725 | 2 |
| C4×D4×D101 | 2 |
| #20265391 | 2 |
| #20265390 | 2 |
| #20265383 | 2 |
| #20265382 | 2 |
| #20265369 | 2 |
| #20265199 | 2 |
| #20265175 | 2 |
| #459×C101 | 2 |
| #3036 | 101 |