Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
192 conjugacy classes of subgroups; only the 72 normal subgroups are shown.
This group has 192 conjugacy classes of subgroups — too many to draw. Only its 72 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. D4×#3624 | C2 | semidirect |
| 2. #11763670 | C2 | semidirect |
| 3. D4⋊#3624 | C2 | semidirect |
| 4. #11763650 | C2 | semidirect |
| 22. D8×C17 | C8 | semidirect |
| 30. D4×C17 | C2×C8 | semidirect |
| 40. C8×C17 | C2×C8 | semidirect |
| 71. C17 | #1580 | semidirect |
| 74. D8 | #3624 | semidirect |
| 86. D4 | C2×#3624 | semidirect |
| 97. C8 | C2×#3624 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D4×#3624 | 2 |
| #11763670 | 2 |
| D4⋊#3624 | 2 |
| #11763650 | 2 |
| D8×Dic17 | 2 |
| #1580 | 17 |