Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
170 conjugacy classes of subgroups; only the 47 normal subgroups are shown.
This group has 170 conjugacy classes of subgroups — too many to draw. Only its 47 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 |
| 3. #20261118 | C2 | semidirect |
| 4. #20260817 | C2 | semidirect |
| 5. #20260553 | C2 | semidirect |
| 6. #20260538 | C2 | semidirect |
| 7. #357×C97 | C2 | semidirect |
| 77. C97 | #2210 | semidirect |
| 84. #357 | D97 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15690755 | 2 |
| C2×#15690751 | 2 |
| #20261118 | 2 |
| #20260817 | 2 |
| #20260553 | 2 |
| #20260538 | 2 |
| #357×C97 | 2 |
| #2210 | 97 |