Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
144 conjugacy classes of subgroups; only the 49 normal subgroups are shown.
This group has 144 conjugacy classes of subgroups — too many to draw. Only its 49 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×#15690755 | C2 | semidirect |
| 2. #20261010 | C2 | semidirect |
| 4. #20260565 | C2 | semidirect |
| 5. #20260552 | C2 | semidirect |
| 6. #20260549 | C2 | semidirect |
| 7. #504×C97 | C2 | semidirect |
| 72. C97 | #2223 | semidirect |
| 74. #504 | D97 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15690755 | 2 |
| #20261010 | 2 |
| #20261005 | 2 |
| #20260565 | 2 |
| #20260552 | 2 |
| #20260549 | 2 |
| #504×C97 | 2 |
| #2223 | 97 |