Finite Group DatabasebetaFinite Group DatabasebetaOrder 12928.
368 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 368 conjugacy classes of subgroups — too many to draw. Only its 85 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 |
|---|---|---|
| 2. C2×#15692188 | C2 | semidirect |
| 3. C2×#15692176 | C2 | semidirect |
| 4. C2×#15692167 | C2 | semidirect |
| 5. #20265034 | C2 | semidirect |
| 6. #20264940 | C2 | semidirect |
| 7. C2×#102×C101 | C2 | semidirect |
| 40. C2×#11717579 | D4 | semidirect |
| 144. C101 | #2033 | semidirect |
| 148. C2×#102 | D101 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15692226 | 2 |
| C2×#15692188 | 2 |
| C2×#15692176 | 2 |
| C2×#15692167 | 2 |
| #20265034 | 2 |
| #20264940 | 2 |
| C2×#102×C101 | 2 |
| #2033 | 101 |