Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
174 conjugacy classes of subgroups; only the 55 normal subgroups are shown.
This group has 174 conjugacy classes of subgroups — too many to draw. Only its 55 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×#15690755 | C2 | semidirect |
| 3. C4×Dic388 | C2 | semidirect |
| 4. #20260537 | C2 | semidirect |
| 5. C4⋊C16×C97 | C2 | semidirect |
| 21. Dic388 | D4 | semidirect |
| 52. C4×C97 | SD32 | semidirect |
| 62. C97 | #2207 | semidirect |
| 66. C4⋊C16 | D97 | semidirect |
| 116. C4 | #15690755 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15690755 | 2 |
| #20261112 | 2 |
| C4×Dic388 | 2 |
| #20260537 | 2 |
| C4⋊C16×C97 | 2 |
| #2207 | 97 |