Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
1018 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 1018 conjugacy classes of subgroups — too many to draw. Only its 165 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. C2×#15690778 | C2 | semidirect |
| 2. #20260922 | C2 | direct (N × H) |
| 3. C2×#15690725 | C2 | semidirect |
| 4. C2×H(5,𝔽2)×C97 | C2 | semidirect |
| 5. C24×D97 | C22 | semidirect |
| 8. #15690778 | C22 | semidirect |
| 9. C2×C22⋊Dic97 | C22 | semidirect |
| 11. #15690725 | C22 | semidirect |
| 13. H(5,𝔽2)×C97 | C22 | semidirect |
| 20. C23×D97 | C23 | semidirect |
| 25. C22⋊Dic97 | C23 | semidirect |
| 28. C24×C97 | D4 | semidirect |
| 38. C2×D4×C97 | D4 | semidirect |
| 41. C22×C4×C97 | D4 | semidirect |
| 50. C23×C97 | C2×D4 | semidirect |
| 66. C2×C4×C97 | C2×D4 | semidirect |
| 91. C2×C97 | B(4,𝔽2) | semidirect |
| 95. C97 | C2×B(4,𝔽2) | semidirect |
| 96. C2×H(5,𝔽2) | D97 | semidirect |
| 102. H(5,𝔽2) | C2×D97 | semidirect |
| 117. C24 | C22⋊D97 | semidirect |
| 129. C2×D4 | C22⋊D97 | semidirect |
| 133. C22×C4 | C22⋊D97 | semidirect |
| 152. C23 | C2×C22⋊D97 | semidirect |
| 164. C2×C4 | C2×C22⋊D97 | semidirect |
| 187. C2 | #20260922 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15690778 | 2 |
| #20260922 | 2 |
| C2×#15690725 | 2 |
| C2×H(5,𝔽2)×C97 | 2 |
| C2×B(4,𝔽2) | 97 |