Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
474 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 474 conjugacy classes of subgroups — too many to draw. Only its 97 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. C22×#13095498 | C2 | semidirect |
| 3. C2×#15690730 | C2 | semidirect |
| 4. #20260490 | C2 | semidirect |
| 5. #391×C97 | C2 | semidirect |
| 31. C2×#11715895 | D4 | semidirect |
| 35. C2×Q8×C97 | D4 | semidirect |
| 57. C2×C4×C97 | SD16 | semidirect |
| 90. C97 | #2014 | semidirect |
| 94. #391 | D97 | semidirect |
| 112. C2×Q8 | D388 | semidirect |
| 152. C2×C4 | #13095498 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#13095498 | 2 |
| C2×#15690807 | 2 |
| C2×#15690730 | 2 |
| #20260490 | 2 |
| #391×C97 | 2 |
| #2014 | 97 |