Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
174 conjugacy classes of subgroups; only the 74 normal subgroups are shown.
This group has 174 conjugacy classes of subgroups — too many to draw. Only its 74 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×#15690883 | C2 | semidirect |
| 2. C22×#13095514 | C2 | semidirect |
| 3. #20261656 | C2 | semidirect |
| 4. #20261630 | C2 | semidirect |
| 5. C22⋊#13095514 | C2 | semidirect |
| 6. #20261621 | C2 | semidirect |
| 24. #13095514 | D4 | semidirect |
| 46. C22⋊D97 | C16 | semidirect |
| 59. C22×C97 | C2×C16 | semidirect |
| 63. C2×D97 | C2×C16 | semidirect |
| 69. Dic97 | C2×C16 | semidirect |
| 76. C97 | D4×C16 | semidirect |
| 138. C22 | #15690883 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15690883 | 2 |
| C22×#13095514 | 2 |
| #20261656 | 2 |
| #20261630 | 2 |
| C22⋊#13095514 | 2 |
| #20261621 | 2 |
| #20260798 | 2 |
| D4×C16 | 97 |