Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
1736 conjugacy classes of subgroups; only the 523 normal subgroups are shown.
This group has 1736 conjugacy classes of subgroups — too many to draw. Only its 523 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×C33×C8 | C2 | semidirect |
| 3. C2×#88850 | C2 | semidirect |
| 4. #11722200 | C2 | semidirect |
| 5. #11722190 | C2 | semidirect |
| 6. #11722185 | C2 | semidirect |
| 7. #11722184 | C2 | semidirect |
| 22. C22×C32×C8 | D3 | semidirect |
| 42. C33×C8 | D4 | semidirect |
| 61. C22×C33 | M16 | semidirect |
| 72. C22×C3×C8 | C3⋊D3 | semidirect |
| 92. C32×C8 | #67 | semidirect |
| 116. C22×C32 | ΓL(1,𝔽25) | semidirect |
| 128. C22×C8 | C3⋊(C3⋊D3) | semidirect |
| 134. C33 | #435 | semidirect |
| 148. C3×C8 | #638 | semidirect |
| 171. C22×C3 | #3743 | semidirect |
| 182. C32 | #5111 | semidirect |
| 198. C8 | #6312 | semidirect |
| 209. C22 | #88850 | semidirect |
| 217. C3 | #10592810 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C33×C8 | 2 |
| C4×#6312 | 2 |
| C2×#88850 | 2 |
| #11722200 | 2 |
| #11722190 | 2 |
| #11722185 | 2 |
| #11722184 | 2 |
| #10592810 | 3 |