Finite Group DatabasebetaFinite Group DatabasebetaOrder 12928.
484 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 484 conjugacy classes of subgroups — too many to draw. Only its 141 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×#15692261 | C2 | semidirect |
| 2. #20265755 | C2 | semidirect |
| 3. #20265420 | C2 | semidirect |
| 4. #20265415 | C2 | semidirect |
| 5. #20265410 | C2 | semidirect |
| 6. C2×#15692189 | C2 | semidirect |
| 7. #20265178 | C2 | semidirect |
| 8. C2×#135×C101 | C2 | semidirect |
| 57. C2×C8×C101 | D4 | semidirect |
| 109. C101 | #3061 | semidirect |
| 110. C2×#135 | D101 | semidirect |
| 161. C2×C8 | C22⋊D101 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15692261 | 2 |
| #20265755 | 2 |
| #20265420 | 2 |
| #20265415 | 2 |
| #20265410 | 2 |
| C2×#15692189 | 2 |
| #20265178 | 2 |
| C2×#135×C101 | 2 |
| #3061 | 101 |