Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
380 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 380 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 |
|---|---|---|
| 3. #20260595 | C2 | semidirect |
| 4. #20260501 | C2 | semidirect |
| 5. #380×C97 | C2 | semidirect |
| 7. C22×C4×D97 | C4 | semidirect |
| 13. C2×#13095490 | C4 | semidirect |
| 16. C2×#13095488 | C4 | semidirect |
| 17. C2×C4×Dic97 | C4 | semidirect |
| 74. C22×D97 | C4⋊C4 | semidirect |
| 101. C2×Dic97 | C4⋊C4 | semidirect |
| 130. C4×C97 | #99 | semidirect |
| 146. C97 | #1799 | semidirect |
| 150. #380 | D97 | semidirect |
| 280. C4 | #15690724 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×C22⋊D97 | 2 |
| C2×#15690724 | 2 |
| #20260595 | 2 |
| #20260501 | 2 |
| #380×C97 | 2 |
| #1799 | 97 |