Finite Group DatabasebetaFinite Group DatabasebetaOrder 12928.
370 conjugacy classes of subgroups; only the 139 normal subgroups are shown.
This group has 370 conjugacy classes of subgroups — too many to draw. Only its 139 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. #20265906 | C2 | semidirect |
| 3. #20265528 | C2 | semidirect |
| 4. #20265463 | C2 | semidirect |
| 7. C8×Q8×C101 | C2 | semidirect |
| 44. Q8×C101 | SD16 | semidirect |
| 75. C101 | #3359 | semidirect |
| 81. C8×Q8 | D101 | semidirect |
| 122. Q8 | #13108063 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20265906 | 2 |
| Q8×D404 | 2 |
| #20265528 | 2 |
| #20265463 | 2 |
| #20265383 | 2 |
| C4×#13108063 | 2 |
| C8×Q8×C101 | 2 |
| #3359 | 101 |