Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
396 conjugacy classes of subgroups; only the 106 normal subgroups are shown.
This group has 396 conjugacy classes of subgroups — too many to draw. Only its 106 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. C2×C8×#87604 | C2 | semidirect |
| 4. C4⋊C4×#87604 | C2 | semidirect |
| 5. #20261609 | C2 | semidirect |
| 6. #20261608 | C2 | semidirect |
| 11. D4×#87604 | C4 | semidirect |
| 17. #15690872 | C4 | semidirect |
| 23. #15690732 | C4 | semidirect |
| 24. #15690731 | C4 | semidirect |
| 25. #15690730 | C4 | semidirect |
| 26. #102×C97 | C4 | semidirect |
| 35. #13095519 | C2×C4 | semidirect |
| 40. C4⋊#87604 | C2×C4 | semidirect |
| 54. C2×#11715895 | C2×C4 | semidirect |
| 57. C4⋊Dic97 | C2×C4 | semidirect |
| 60. C2×C8×C97 | C2×C4 | semidirect |
| 61. C4⋊C4×C97 | C2×C4 | semidirect |
| 85. D4×C97 | C42 | semidirect |
| 93. D388 | C42 | semidirect |
| 123. #87604 | #102 | direct (N × H) |
| 140. C97 | C4×#102 | semidirect |
| 164. #102 | #87604 | direct (N × H) |
| 190. C2×C8 | C2×#87604 | semidirect |
| 197. C4⋊C4 | C2×#87604 | semidirect |
| 216. D4 | C4×#87604 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D4×#87604 | 2 |
| C2×#15690872 | 2 |
| C2×C8×#87604 | 2 |
| C4⋊C4×#87604 | 2 |
| #20261609 | 2 |
| #20261608 | 2 |
| #102×D97 | 2 |
| C4×#102 | 97 |