Finite Group DatabasebetaFinite Group DatabasebetaOrder 27904.
436 conjugacy classes of subgroups; only the 102 normal subgroups are shown.
This group has 436 conjugacy classes of subgroups — too many to draw. Only its 102 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C23×C109 | #120 |
| commutator, Frattini, cosocle | C2×C42 | C23×C109 |
| LCS | G ▷ C2×C42 ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C23×C109 ◁ C2×C42×C109 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 74. C2×Q8×C109 | Q16 | semidirect |
| 109. C4⋊C4×C109 | Q16 | semidirect |
| 177. #7784 | C109 | direct (N × H) |
| 192. C109 | #7784 | direct (N × H) |
| 259. C2×Q8 | Q16×C109 | semidirect |
| 294. C4⋊C4 | Q16×C109 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C109×#2806 | 2 |
| C109×#2057 | 2 |
| C109×#2024 | 2 |
| C109×#2016 | 2 |
| C109×#1272 | 2 |
| C109×#1271 | 2 |
| #7784 | 109 |