Finite Group DatabasebetaFinite Group DatabasebetaOrder 12928.
228 conjugacy classes of subgroups; only the 59 normal subgroups are shown.
This group has 228 conjugacy classes of subgroups — too many to draw. Only its 59 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. Q8×Dic202 | C2 | semidirect |
| 5. #20264925 | C2 | semidirect |
| 6. #20264909 | C2 | semidirect |
| 7. Q8⋊C8×C101 | C2 | semidirect |
| 52. Q8×C101 | SD16 | semidirect |
| 69. Dic202 | SD16 | semidirect |
| 92. C101 | #1623 | semidirect |
| 99. Q8⋊C8 | D101 | semidirect |
| 148. Q8 | #13108063 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×Dic202 | 2 |
| #20265550 | 2 |
| #20265378 | 2 |
| #20265377 | 2 |
| #20264925 | 2 |
| #20264909 | 2 |
| Q8⋊C8×C101 | 2 |
| #1623 | 101 |