Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
500 conjugacy classes of subgroups; only the 166 normal subgroups are shown.
This group has 500 conjugacy classes of subgroups — too many to draw. Only its 166 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×#15690898 | C2 | semidirect |
| 2. C2×#15690897 | C2 | semidirect |
| 3. #20261768 | C2 | semidirect |
| 4. #20261762 | C2 | semidirect |
| 5. #20261740 | C2 | semidirect |
| 6. #20261710 | C2 | semidirect |
| 7. #20261709 | C2 | semidirect |
| 8. C4×#13095519 | C2 | semidirect |
| 40. #13095519 | D4 | semidirect |
| 107. Dic97 | #131 | semidirect |
| 116. C97 | #2931 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15690898 | 2 |
| C2×#15690897 | 2 |
| #20261768 | 2 |
| #20261762 | 2 |
| #20261740 | 2 |
| #20261710 | 2 |
| #20261709 | 2 |
| C4×#13095519 | 2 |
| #20261284 | 2 |
| #2931 | 97 |