Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
572 conjugacy classes of subgroups; only the 153 normal subgroups are shown.
This group has 572 conjugacy classes of subgroups — too many to draw. Only its 153 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×#15690832 | C2 | semidirect |
| 2. C2×#15690830 | C2 | semidirect |
| 3. #20261281 | C2 | semidirect |
| 4. #20261120 | C2 | semidirect |
| 5. #20261118 | C2 | semidirect |
| 6. #20261116 | C2 | semidirect |
| 7. #20261113 | C2 | semidirect |
| 8. #20261110 | C2 | semidirect |
| 9. #20261106 | C2 | semidirect |
| 10. C2×C8×Dic97 | C2 | semidirect |
| 11. C2×#135×C97 | C2 | semidirect |
| 55. C2×#11715895 | D4 | semidirect |
| 74. C2×C8×C97 | D4 | semidirect |
| 119. Dic97 | #135 | semidirect |
| 126. C97 | #3147 | semidirect |
| 129. C2×#135 | D97 | semidirect |
| 194. C2×C8 | C22⋊D97 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15690832 | 2 |
| C2×#15690830 | 2 |
| #20261281 | 2 |
| #20261120 | 2 |
| #20261118 | 2 |
| #20261116 | 2 |
| #20261113 | 2 |
| #20261110 | 2 |
| #20261106 | 2 |
| C2×C8×Dic97 | 2 |
| C2×#135×C97 | 2 |
| #3147 | 97 |