Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
396 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 396 conjugacy classes of subgroups — too many to draw. Only its 95 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. C2×C9×ΓL(1,𝔽25) | C2 | semidirect |
| 2. C2×C3×#3664 | C2 | semidirect |
| 4. #11720960 | C2 | semidirect |
| 5. #11720541 | C2 | semidirect |
| 6. #11720283 | C2 | semidirect |
| 7. #11720276 | C2 | semidirect |
| 33. C2×#3664 | D3 | semidirect |
| 52. C3×C8×C9 | D4 | semidirect |
| 105. C2×ΓL(1,𝔽25) | D9 | semidirect |
| 148. C8×C9 | #67 | semidirect |
| 222. C3×C9 | #468 | semidirect |
| 256. C3×C8 | #611 | semidirect |
| 318. C9 | #5174 | semidirect |
| 334. C8 | #6194 | semidirect |
| 362. C3 | #10588816 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C9×ΓL(1,𝔽25) | 2 |
| C2×C3×#3664 | 2 |
| #11721037 | 2 |
| #11720960 | 2 |
| #11720541 | 2 |
| #11720283 | 2 |
| #11720276 | 2 |
| #10590833 | 3 |
| #10588816 | 3 |