Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
672 conjugacy classes of subgroups; only the 189 normal subgroups are shown.
This group has 672 conjugacy classes of subgroups — too many to draw. Only its 189 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. #20260626 | C2 | semidirect |
| 3. #20260624 | C2 | semidirect |
| 4. #20260593 | C2 | semidirect |
| 6. C4×C22⋊Dic97 | C2 | semidirect |
| 7. C4×C22⋊C4×C97 | C2 | semidirect |
| 10. C2×#13095490 | C22 | semidirect |
| 12. C2×#13095488 | C4 | semidirect |
| 17. C2×C4×Dic97 | C22 | semidirect |
| 18. #15690717 | C22 | semidirect |
| 19. #15690717 | C22 | semidirect |
| 22. C2×C42×C97 | C22 | semidirect |
| 23. #95×C97 | C22 | semidirect |
| 100. C97 | #2312 | semidirect |
| 107. C4×C22⋊C4 | D97 | semidirect |
| 120. C2×C42 | C2×D97 | semidirect |
| 123. #95 | C2×D97 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#13095488 | 2 |
| #20260626 | 2 |
| #20260624 | 2 |
| #20260593 | 2 |
| #20260590 | 2 |
| C4×C22⋊Dic97 | 2 |
| C4×C22⋊C4×C97 | 2 |
| #2312 | 97 |