Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
680 conjugacy classes of subgroups; only the 365 normal subgroups are shown.
This group has 680 conjugacy classes of subgroups — too many to draw. Only its 365 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×#15690721 | C2 | semidirect |
| 4. C2×#15690720 | C2 | semidirect |
| 5. #97×D97 | C2 | direct (N × H) |
| 6. C2×#97×C97 | C2 | semidirect |
| 10. C2×C8×D97 | C4 | semidirect |
| 16. #15690721 | C22 | semidirect |
| 17. #15690720 | C22 | semidirect |
| 20. #97×C97 | C22 | semidirect |
| 29. C2×#11715895 | C2×C4 | semidirect |
| 31. C8×D97 | C2×C4 | semidirect |
| 37. C2×C8×C97 | C2×C4 | semidirect |
| 57. C8×C97 | C22×C4 | semidirect |
| 58. #11715895 | C22×C4 | semidirect |
| 62. C2×D97 | #97 | direct (N × H) |
| 70. C2×C97 | C2×#97 | semidirect |
| 73. D97 | C2×#97 | direct (N × H) |
| 75. C97 | C22×#97 | semidirect |
| 81. C2×#97 | D97 | direct (N × H) |
| 95. #97 | C2×D97 | direct (N × H) |
| 109. C2×C8 | C4×D97 | semidirect |
| 133. C8 | C2×C4×D97 | semidirect |
| 146. C2 | #97×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×C42×D97 | 2 |
| C2×#15690721 | 2 |
| C2×#15690720 | 2 |
| #97×D97 | 2 |
| C2×#97×C97 | 2 |
| C22×#97 | 97 |