Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
500 conjugacy classes of subgroups; only the 225 normal subgroups are shown.
This group has 500 conjugacy classes of subgroups — too many to draw. Only its 225 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. #41×Dic97 | C2 | semidirect |
| 2. Q16×Dic97 | C2 | semidirect |
| 3. SD16×Dic97 | C2 | semidirect |
| 4. D8×Dic97 | C2 | semidirect |
| 5. #20260773 | C2 | semidirect |
| 6. #20260731 | C2 | semidirect |
| 7. C2×C8×Dic97 | C2 | semidirect |
| 24. #135×C97 | C4 | semidirect |
| 43. #41×C97 | C2×C4 | semidirect |
| 49. Q16×C97 | C2×C4 | semidirect |
| 50. SD16×C97 | C2×C4 | semidirect |
| 51. D8×C97 | C2×C4 | semidirect |
| 52. C2×C8×C97 | C2×C4 | semidirect |
| 87. Dic97 | #135 | direct (N × H) |
| 93. C97 | C4×#135 | semidirect |
| 103. #135 | Dic97 | direct (N × H) |
| 123. #41 | C2×Dic97 | semidirect |
| 131. Q16 | C2×Dic97 | semidirect |
| 132. SD16 | C2×Dic97 | semidirect |
| 133. D8 | C2×Dic97 | semidirect |
| 136. C2×C8 | C2×Dic97 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #41×Dic97 | 2 |
| Q16×Dic97 | 2 |
| SD16×Dic97 | 2 |
| D8×Dic97 | 2 |
| #20260773 | 2 |
| #20260731 | 2 |
| C2×C8×Dic97 | 2 |
| C2×#135×C97 | 2 |
| C4×#135 | 97 |