Finite Group DatabasebetaFinite Group DatabasebetaOrder 12928.
380 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 380 conjugacy classes of subgroups — too many to draw. Only its 121 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. #20265712 | C2 | semidirect |
| 2. #20265561 | C2 | semidirect |
| 3. #20265534 | C2 | semidirect |
| 4. #20265419 | C2 | semidirect |
| 6. #20265407 | C2 | semidirect |
| 7. #20265271 | C2 | semidirect |
| 8. #20265264 | C2 | semidirect |
| 9. #20265259 | C2 | semidirect |
| 10. C4×C8×D101 | C2 | semidirect |
| 11. #499×C101 | C2 | semidirect |
| 119. C101 | #3168 | semidirect |
| 121. #499 | D101 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20265712 | 2 |
| #20265561 | 2 |
| #20265534 | 2 |
| #20265419 | 2 |
| #20265414 | 2 |
| #20265407 | 2 |
| #20265271 | 2 |
| #20265264 | 2 |
| #20265259 | 2 |
| C4×C8×D101 | 2 |
| #499×C101 | 2 |
| #3168 | 101 |