Finite Group DatabasebetaFinite Group DatabasebetaOrder 26368.
252 conjugacy classes of subgroups; only the 86 normal subgroups are shown.
This group has 252 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×C103 | #466 |
| commutator, Frattini, cosocle | C4×C8 | C23×C103 |
| prime radical | C103×#1667 | C2 |
| LCS | G ▷ C4×C8 ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C103 ◁ C42×C103 ◁ C8×D4×C103 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C103×#2248 | C2 | semidirect |
| 2. D4×C16×C103 | C2 | semidirect |
| 3. C103×#1669 | C2 | semidirect |
| 5. C103×#1372 | C2 | semidirect |
| 6. C103×#1362 | C2 | semidirect |
| 7. C103×#1361 | C2 | semidirect |
| 73. C16×C103 | D8 | semidirect |
| 84. D4×C103 | SD32 | semidirect |
| 112. #12432 | C103 | direct (N × H) |
| 118. #2248 | C2×C103 | semidirect |
| 119. D4×C16 | C2×C103 | semidirect |
| 120. #1669 | C2×C103 | semidirect |
| 122. #1372 | C2×C103 | semidirect |
| 123. #1362 | C2×C103 | semidirect |
| 124. #1361 | C2×C103 | semidirect |
| 125. C103 | #12432 | direct (N × H) |
| 191. C16 | D8×C103 | semidirect |
| 202. D4 | SD32×C103 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C103×#2248 | 2 |
| D4×C16×C103 | 2 |
| C103×#1669 | 2 |
| C103×#1667 | 2 |
| C103×#1372 | 2 |
| C103×#1362 | 2 |
| C103×#1361 | 2 |
| #12432 | 103 |