Finite Group DatabasebetaFinite Group DatabasebetaOrder 27904.
600 conjugacy classes of subgroups; only the 114 normal subgroups are shown.
This group has 600 conjugacy classes of subgroups — too many to draw. Only its 114 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C109 | #120 |
| commutator, Frattini, cosocle | C2×C42 | C23×C109 |
| prime radical | C109×#2819 | C2 |
| LCS | G ▷ C2×C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C23×C109 ◁ C2×C42×C109 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#489×C109 | C2 | semidirect |
| 3. C109×#1960 | C2 | semidirect |
| 4. C2×#329×C109 | C2 | semidirect |
| 5. C109×#1295 | C2 | semidirect |
| 28. C4⋊Q8×C109 | D4 | semidirect |
| 44. #97×C109 | D4 | semidirect |
| 126. #10085 | C109 | direct (N × H) |
| 132. C2×#489 | C2×C109 | semidirect |
| 134. #1960 | C2×C109 | semidirect |
| 135. C2×#329 | C2×C109 | semidirect |
| 136. #1295 | C2×C109 | semidirect |
| 137. C109 | #10085 | direct (N × H) |
| 160. C4⋊Q8 | D4×C109 | semidirect |
| 176. #97 | D4×C109 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#489×C109 | 2 |
| C109×#2819 | 2 |
| C109×#1960 | 2 |
| C2×#329×C109 | 2 |
| C109×#1295 | 2 |
| #10085 | 109 |