Finite Group DatabasebetaFinite Group DatabasebetaOrder 27904.
390 conjugacy classes of subgroups; only the 86 normal subgroups are shown.
This group has 390 conjugacy classes of subgroups — too many to draw. Only its 86 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 |
| LCS | G ▷ C4×C8 ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C109 ◁ C42×C109 ◁ C8×D4×C109 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C109×#3283 | C2 | semidirect |
| 2. C109×#2248 | C2 | semidirect |
| 3. C109×#2206 | C2 | semidirect |
| 4. C109×#1667 | C2 | semidirect |
| 5. C109×#1362 | C2 | semidirect |
| 6. C109×#1331 | C2 | semidirect |
| 7. C109×D4⋊C16 | C2 | semidirect |
| 77. D8×C109 | D8 | semidirect |
| 144. #12319 | C109 | direct (N × H) |
| 151. #3283 | C2×C109 | semidirect |
| 152. #2248 | C2×C109 | semidirect |
| 153. #2206 | C2×C109 | semidirect |
| 154. #1667 | C2×C109 | semidirect |
| 155. #1362 | C2×C109 | semidirect |
| 156. #1331 | C2×C109 | semidirect |
| 157. D4⋊C16 | C2×C109 | semidirect |
| 158. C109 | #12319 | direct (N × H) |
| 228. D8 | D8×C109 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C109×#3283 | 2 |
| C109×#2248 | 2 |
| C109×#2206 | 2 |
| C109×#1667 | 2 |
| C109×#1362 | 2 |
| C109×#1331 | 2 |
| C109×D4⋊C16 | 2 |
| #12319 | 109 |