Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
360 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 115 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 |
|---|---|---|
| 2. C2×Q16×D97 | C2 | semidirect |
| 3. #20261178 | C2 | semidirect |
| 4. #20261177 | C2 | semidirect |
| 5. #20261176 | C2 | semidirect |
| 6. #20261175 | C2 | semidirect |
| 7. #20261174 | C2 | semidirect |
| 8. Q32×D97 | C2 | semidirect |
| 9. SD32×D97 | C2 | semidirect |
| 10. M32×D97 | C2 | semidirect |
| 11. #510×C97 | C2 | semidirect |
| 19. C2×Dic388 | C22 | semidirect |
| 25. Q16×D97 | C22 | semidirect |
| 29. Dic776 | C22 | semidirect |
| 30. #15690756 | C22 | semidirect |
| 31. #15690756 | C22 | semidirect |
| 32. #15690755 | C22 | semidirect |
| 33. #15690754 | C22 | semidirect |
| 34. #15690753 | C22 | semidirect |
| 35. #15690750 | C22 | semidirect |
| 36. #15690749 | C22 | semidirect |
| 39. C2×Q16×C97 | C22 | semidirect |
| 40. Q32×C97 | C22 | semidirect |
| 41. SD32×C97 | C22 | semidirect |
| 42. M32×C97 | C22 | semidirect |
| 143. D97 | #510 | direct (N × H) |
| 145. C97 | C2×#510 | semidirect |
| 153. #510 | D97 | direct (N × H) |
| 172. C2×Q16 | C2×D97 | semidirect |
| 179. Q32 | C2×D97 | semidirect |
| 183. SD32 | C2×D97 | semidirect |
| 186. M32 | C2×D97 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #135×D97 | 2 |
| C2×Q16×D97 | 2 |
| #20261178 | 2 |
| #20261177 | 2 |
| #20261176 | 2 |
| #20261175 | 2 |
| #20261174 | 2 |
| Q32×D97 | 2 |
| SD32×D97 | 2 |
| M32×D97 | 2 |
| #510×C97 | 2 |
| C2×#510 | 97 |