Finite Group DatabasebetaFinite Group DatabasebetaOrder 27904.
912 conjugacy classes of subgroups; only the 130 normal subgroups are shown.
This group has 912 conjugacy classes of subgroups — too many to draw. Only its 130 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 | #392 |
| commutator, Frattini, cosocle | C2×C42 | C23×C109 |
| prime radical | C109×#2867 | C2 |
| LCS | G ▷ C2×C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C109 ◁ C2×C42×C109 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C109×#3208 | C2 | semidirect |
| 3. C109×#1994 | C2 | semidirect |
| 4. C109×#1545 | C2 | semidirect |
| 5. C109×#1276 | C2 | semidirect |
| 25. C4⋊Q8×C109 | D4 | semidirect |
| 41. C4⋊C8×C109 | D4 | semidirect |
| 73. C42×C109 | SD16 | semidirect |
| 117. #10290 | C109 | direct (N × H) |
| 122. #3208 | C2×C109 | semidirect |
| 124. #1994 | C2×C109 | semidirect |
| 125. #1545 | C2×C109 | semidirect |
| 126. #1276 | C2×C109 | semidirect |
| 127. C109 | #10290 | direct (N × H) |
| 147. C4⋊Q8 | D4×C109 | semidirect |
| 163. C4⋊C8 | D4×C109 | semidirect |
| 195. C42 | SD16×C109 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C109×#3208 | 2 |
| C109×#2867 | 2 |
| C109×#1994 | 2 |
| C109×#1545 | 2 |
| C109×#1276 | 2 |
| #10290 | 109 |