Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
336 conjugacy classes of subgroups; only the 94 normal subgroups are shown.
This group has 336 conjugacy classes of subgroups — too many to draw. Only its 94 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×#15690879 | C2 | semidirect |
| 3. #20261609 | C2 | semidirect |
| 10. C22×#11715895 | C4 | semidirect |
| 12. C2×C8×D97 | C4 | semidirect |
| 13. C2×C8×D97 | C4 | semidirect |
| 16. C22×C8×C97 | C4 | semidirect |
| 64. C8×C97 | C22⋊C4 | semidirect |
| 66. #11715895 | C22⋊C4 | semidirect |
| 69. C22×C97 | #107 | semidirect |
| 75. C2×D97 | #107 | semidirect |
| 94. C97 | #1808 | semidirect |
| 106. C22×C8 | #87604 | semidirect |
| 160. C8 | C22⋊#87604 | semidirect |
| 172. C22 | #15690879 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15690879 | 2 |
| #20261677 | 2 |
| #20261609 | 2 |
| C22×C8×D97 | 2 |
| #1808 | 97 |