Finite Group DatabasebetaFinite Group DatabasebetaOrder 27904.
286 conjugacy classes of subgroups; only the 82 normal subgroups are shown.
This group has 286 conjugacy classes of subgroups — too many to draw. Only its 82 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C109 | #447 |
| commutator, Frattini, cosocle | C4×C8 | C23×C109 |
| prime radical | C2×D8×C109 | D4 |
| LCS | G ▷ C4×C8 ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C109 ◁ C42×C109 ◁ #446×C109 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C109×#2255 | C2 | semidirect |
| 4. C109×#1694 | C2 | semidirect |
| 5. C109×#1363 | C2 | semidirect |
| 6. C109×#1338 | C2 | semidirect |
| 69. D8×C109 | Q16 | semidirect |
| 131. #12414 | C109 | direct (N × H) |
| 137. #2255 | C2×C109 | semidirect |
| 139. #1694 | C2×C109 | semidirect |
| 140. #1363 | C2×C109 | semidirect |
| 141. #1338 | C2×C109 | semidirect |
| 143. C109 | #12414 | direct (N × H) |
| 205. D8 | Q16×C109 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C109×#3389 | 2 |
| C109×#2255 | 2 |
| C109×#2226 | 2 |
| C109×#1694 | 2 |
| C109×#1363 | 2 |
| C109×#1338 | 2 |
| C109×#1333 | 2 |
| #12414 | 109 |