Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
374 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 374 conjugacy classes of subgroups — too many to draw. Only its 113 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×#15690734 | C2 | semidirect |
| 5. #20260497 | C2 | semidirect |
| 6. #20260490 | C2 | semidirect |
| 7. C2×C4×Q8×C97 | C2 | semidirect |
| 11. C2×#13095498 | C4 | semidirect |
| 73. Q8×C97 | C22⋊C4 | semidirect |
| 85. C2×C4×C97 | SD16 | semidirect |
| 133. C97 | #1880 | semidirect |
| 135. C2×C4×Q8 | D97 | semidirect |
| 206. Q8 | #13095488 | semidirect |
| 225. 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×#15690734 | 2 |
| C2×#15690730 | 2 |
| #20260637 | 2 |
| #20260497 | 2 |
| #20260490 | 2 |
| C2×C4×Q8×C97 | 2 |
| #1880 | 97 |