Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
600 conjugacy classes of subgroups; only the 269 normal subgroups are shown.
This group has 600 conjugacy classes of subgroups — too many to draw. Only its 269 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×#15690742 | C2 | semidirect |
| 4. C2×#15690741 | C2 | semidirect |
| 5. #106×D97 | C2 | direct (N × H) |
| 6. C2×#106×C97 | C2 | semidirect |
| 10. C2×C8×D97 | C4 | semidirect |
| 16. #15690742 | C22 | semidirect |
| 17. #15690741 | C22 | semidirect |
| 20. #106×C97 | C22 | semidirect |
| 30. C2×#11715895 | C2×C4 | semidirect |
| 32. C8×D97 | C2×C4 | semidirect |
| 38. C2×C8×C97 | C2×C4 | semidirect |
| 60. C8×C97 | C22×C4 | semidirect |
| 61. #11715895 | C22×C4 | semidirect |
| 65. C2×D97 | #106 | direct (N × H) |
| 74. C2×C97 | C2×#106 | semidirect |
| 77. D97 | C2×#106 | direct (N × H) |
| 79. C97 | C22×#106 | semidirect |
| 85. C2×#106 | D97 | direct (N × H) |
| 99. #106 | C2×D97 | direct (N × H) |
| 114. C2×C8 | C4×D97 | semidirect |
| 140. C8 | C2×C4×D97 | semidirect |
| 154. C2 | #106×D97 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C8×D97 | 2 |
| C2×C4⋊C4×D97 | 2 |
| C2×#15690742 | 2 |
| C2×#15690741 | 2 |
| #106×D97 | 2 |
| C2×#106×C97 | 2 |
| C22×#106 | 97 |