Finite Group DatabasebetaFinite Group DatabasebetaOrder 12928.
482 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 482 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×#15692278 | C2 | semidirect |
| 2. C2×Q16×D101 | C2 | semidirect |
| 3. #20265839 | C2 | semidirect |
| 4. #20265561 | C2 | semidirect |
| 5. #20265419 | C2 | semidirect |
| 6. #20265414 | C2 | semidirect |
| 7. #20265399 | C2 | semidirect |
| 8. #20265342 | C2 | semidirect |
| 9. #20265317 | C2 | semidirect |
| 10. C8×D404 | C2 | semidirect |
| 11. C4×Q16×C101 | C2 | semidirect |
| 73. Q16×C101 | D4 | semidirect |
| 120. C2×D101 | #135 | semidirect |
| 137. C101 | #3285 | semidirect |
| 147. C4×Q16 | D101 | semidirect |
| 195. Q16 | D404 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15692278 | 2 |
| C2×Q16×D101 | 2 |
| #20265839 | 2 |
| #20265561 | 2 |
| #20265419 | 2 |
| #20265414 | 2 |
| #20265399 | 2 |
| #20265342 | 2 |
| #20265317 | 2 |
| C8×D404 | 2 |
| C4×Q16×C101 | 2 |
| #3285 | 101 |