Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
368 conjugacy classes of subgroups; only the 213 normal subgroups are shown.
This group has 368 conjugacy classes of subgroups — too many to draw. Only its 213 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. #20261153 | C2 | direct (N × H) |
| 3. C2×#15690749 | C2 | semidirect |
| 4. C22×#13095486 | C2 | semidirect |
| 5. C2×C16×D97 | C2 | semidirect |
| 6. C2×M32×C97 | C2 | semidirect |
| 13. #15690749 | C22 | semidirect |
| 16. C2×#13095486 | C22 | semidirect |
| 17. C16×D97 | C22 | semidirect |
| 19. M32×C97 | C22 | semidirect |
| 66. C2×C97 | #504 | semidirect |
| 70. C97 | C2×#504 | semidirect |
| 74. C2×M32 | D97 | semidirect |
| 85. M32 | C2×D97 | semidirect |
| 137. C2 | #20261153 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15690816 | 2 |
| #20261153 | 2 |
| C2×#15690749 | 2 |
| C22×#13095486 | 2 |
| C2×C16×D97 | 2 |
| C2×M32×C97 | 2 |
| C2×#504 | 97 |