Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
552 conjugacy classes of subgroups; only the 194 normal subgroups are shown.
This group has 552 conjugacy classes of subgroups — too many to draw. Only its 194 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. C22×#63247 | C2 | semidirect |
| 2. #11763844 | C2 | direct (N × H) |
| 3. C2×C4⋊#3624 | C2 | semidirect |
| 4. C2×C22⋊#3624 | C2 | semidirect |
| 5. C2×C4×#3624 | C2 | semidirect |
| 10. C2×#63247 | C22 | semidirect |
| 19. C22⋊#3624 | C22 | semidirect |
| 20. C4⋊#3624 | C22 | semidirect |
| 21. C4×#3624 | C22 | semidirect |
| 36. C2×#3624 | D4 | semidirect |
| 50. C2×C4×C17 | M16 | semidirect |
| 65. #3624 | C2×D4 | semidirect |
| 75. C4×C17 | C2×M16 | semidirect |
| 88. C2×C17 | #436 | semidirect |
| 107. C17 | C2×#436 | semidirect |
| 147. C2×C4 | #63247 | semidirect |
| 165. C4 | C2×#63247 | semidirect |
| 167. C2 | #11763844 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#63247 | 2 |
| #11763844 | 2 |
| C2×C4⋊#3624 | 2 |
| C2×C22⋊#3624 | 2 |
| C2×C4×#3624 | 2 |
| C2×D4×Dic17 | 2 |
| C2×#436 | 17 |