Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
1072 conjugacy classes of subgroups; only the 258 normal subgroups are shown.
This group has 1072 conjugacy classes of subgroups — too many to draw. Only its 258 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. C22×#13095519 | C2 | semidirect |
| 2. C22×C4⋊#87604 | C2 | semidirect |
| 3. C2×#15690872 | C2 | direct (N × H) |
| 7. C2×#13095519 | C22 | semidirect |
| 10. C2×C4⋊#87604 | C22 | semidirect |
| 11. #15690872 | C22 | direct (N × H) |
| 13. C22×D388 | C4 | semidirect |
| 17. C2×D4×D97 | C4 | semidirect |
| 20. C22×D4×C97 | C4 | semidirect |
| 24. #13095519 | C23 | semidirect |
| 27. C4⋊#87604 | C23 | semidirect |
| 35. C2×D388 | C2×C4 | semidirect |
| 41. D4×D97 | C2×C4 | semidirect |
| 50. C2×D4×C97 | C2×C4 | semidirect |
| 69. D4×C97 | C22×C4 | semidirect |
| 77. D388 | C22×C4 | semidirect |
| 86. C22×C97 | #102 | semidirect |
| 93. C2×D97 | #102 | semidirect |
| 104. C2×C97 | C2×#102 | semidirect |
| 107. D97 | C2×#102 | semidirect |
| 111. C97 | C22×#102 | semidirect |
| 123. C22×D4 | #87604 | semidirect |
| 149. C2×D4 | C2×#87604 | semidirect |
| 182. D4 | C22×#87604 | semidirect |
| 207. C22 | #15690872 | direct (N × H) |
| 219. C2 | C2×#15690872 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#13095519 | 2 |
| C22×C4⋊#87604 | 2 |
| C2×#15690872 | 2 |
| C22×D4×D97 | 2 |
| C22×#102 | 97 |