Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
182 conjugacy classes of subgroups; only the 58 normal subgroups are shown.
This group has 182 conjugacy classes of subgroups — too many to draw. Only its 58 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. #11763843 | C2 | semidirect |
| 2. D4×#3624 | C2 | semidirect |
| 3. #11763672 | C2 | semidirect |
| 4. #11763657 | C2 | semidirect |
| 5. D4⋊#3624 | C2 | semidirect |
| 6. #11763651 | C2 | semidirect |
| 45. D4×C17 | M16 | semidirect |
| 61. #3624 | D8 | semidirect |
| 106. C17 | #1581 | semidirect |
| 131. D4 | #63243 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11763843 | 2 |
| D4×#3624 | 2 |
| #11763672 | 2 |
| #11763657 | 2 |
| D4⋊#3624 | 2 |
| #11763651 | 2 |
| #11762889 | 2 |
| #1581 | 17 |