Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
500 conjugacy classes of subgroups; only the 244 normal subgroups are shown.
This group has 500 conjugacy classes of subgroups — too many to draw. Only its 244 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. #11763825 | C2 | semidirect |
| 3. C2×C22⋊#3624 | C2 | semidirect |
| 7. C22×#3624 | C22 | semidirect |
| 14. C22⋊#3624 | C22 | semidirect |
| 15. C4⋊#3624 | C22 | semidirect |
| 16. C4×#3624 | C22 | semidirect |
| 18. C2×D4×C17 | C8 | semidirect |
| 35. C23×C17 | C2×C8 | semidirect |
| 38. D4×C17 | C2×C8 | semidirect |
| 39. C2×C4×C17 | C2×C8 | semidirect |
| 86. C17 | #2972 | semidirect |
| 88. C2×D4 | #3624 | semidirect |
| 105. C23 | C2×#3624 | semidirect |
| 108. D4 | C2×#3624 | semidirect |
| 118. C2×C4 | 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 |
| #11763825 | 2 |
| C2×C22⋊#3624 | 2 |
| C2×D4×Dic17 | 2 |
| #2972 | 17 |