Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
360 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 121 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. M16×Dic97 | C2 | semidirect |
| 4. C42×Dic97 | C2 | semidirect |
| 5. #20260496 | C2 | semidirect |
| 6. #20260495 | C2 | semidirect |
| 9. Q8×Dic97 | C4 | semidirect |
| 11. D4×Dic97 | C4 | semidirect |
| 18. #15690737 | C4 | semidirect |
| 24. #104×C97 | C4 | semidirect |
| 29. #13095495 | C2×C4 | semidirect |
| 40. C4×Dic97 | C2×C4 | semidirect |
| 54. M16×C97 | C2×C4 | semidirect |
| 57. C42×C97 | C2×C4 | semidirect |
| 61. Q8×C97 | C42 | semidirect |
| 65. D4×C97 | C42 | semidirect |
| 101. Dic97 | #104 | direct (N × H) |
| 108. C97 | C4×#104 | semidirect |
| 130. #104 | Dic97 | direct (N × H) |
| 149. M16 | C2×Dic97 | semidirect |
| 165. C42 | C2×Dic97 | semidirect |
| 169. Q8 | C4×Dic97 | semidirect |
| 173. D4 | C4×Dic97 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #41×Dic97 | 2 |
| C2×#15690737 | 2 |
| M16×Dic97 | 2 |
| C42×Dic97 | 2 |
| #20260496 | 2 |
| #20260495 | 2 |
| C2×#104×C97 | 2 |
| C4×#104 | 97 |