Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
592 conjugacy classes of subgroups; only the 157 normal subgroups are shown.
This group has 592 conjugacy classes of subgroups — too many to draw. Only its 157 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×#15690734 | C2 | semidirect |
| 14. C22×Q8×C97 | C4 | semidirect |
| 49. Q8×C97 | C22⋊C4 | semidirect |
| 68. C22×C97 | #103 | semidirect |
| 86. C97 | #1787 | semidirect |
| 94. C22×Q8 | Dic97 | semidirect |
| 135. Q8 | C22⋊Dic97 | semidirect |
| 154. C22 | #15690734 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15690734 | 2 |
| C2×C22⋊#11715895 | 2 |
| #20260595 | 2 |
| C23×Q8×C97 | 2 |
| #1787 | 97 |