Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
436 conjugacy classes of subgroups; only the 98 normal subgroups are shown.
This group has 436 conjugacy classes of subgroups — too many to draw. Only its 98 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×#15690872 | C2 | semidirect |
| 2. C4×#13095519 | C2 | semidirect |
| 3. #20261681 | C2 | semidirect |
| 12. #15690807 | C4 | semidirect |
| 14. #15690806 | C4 | semidirect |
| 16. #127×C97 | C4 | semidirect |
| 19. #13095519 | D4 | semidirect |
| 76. C4×C97 | #102 | semidirect |
| 78. Dic97 | #102 | semidirect |
| 88. C97 | #1957 | semidirect |
| 99. #127 | #87604 | semidirect |
| 166. C4 | #15690872 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15690872 | 2 |
| C4×#13095519 | 2 |
| #20261681 | 2 |
| #127×D97 | 2 |
| #1957 | 97 |